Admittedly, it's kind of tough to talk about To the Lighthouse in terms of plot trajectory because, while time does certainly move in the novel, "plot" would seem to suggest that there's some sort of definite goal to the narrative. And yet, really, the book seems like it might be more of a three-part portrait than a real beginning-middle-end kind of story. Still, there are two characters who do have something approaching plot: Lily Briscoe and James Ramsay. Both are actively striving for something, so we're going to organize our plot analysis to see what they actually get.
At the start of Part One ("The Window"), James Ramsay is six, Lily Briscoe, thirty-four. James is the baby of the Ramsay family and much-beloved by his mother, but he feels fiercely competitive with his father, who occupies a place in Mrs. Ramsay's life that James cannot hope to occupy. Lily Briscoe, on the other hand, is an impoverished friend of the Ramsay family whose uncertain social place is due to the fact that she's thirty-four, unmarried, and not very conventionally attractive. Not a good situation for a woman in the 1920s to be in. But she has a strong, mutually affectionate relationship with Mrs. Ramsay that sustains her throughout her stay with the Ramsay family on the Isle of Skye.
James's desire to go to the Lighthouse – and his father's (and Charles Tansley's) insistence on refusing – is the main conflict through which James's difficult relationship with his oppressive father gets represented. Mr. Ramsay wants all of his children to behave on his terms and to strive according to his orders. James's rebelliousness shows that the main conflict of James's life is going to be with his father and his father's power over James's life.
Lily Briscoe, like James, is sadly squelched by a man with more status than she has – Charles Tansley. She wants to paint, but to do so seems to be a threat to the masculine system of intellectual hierarchy that both Mr. Ramsay and Charles Tansley rely upon. Lily's trying to find a way, as a woman, to pursue her own artistic development freely, but she's meeting lots of obstacles along the way because of her gender and relatively low social status.
The beautiful, charming, perhaps secretly frustrated Mrs. Ramsay seems at first like one possible alternative to the oppressive Mr. Ramsay. But 1) Mr. Ramsay turns out not to be all that bad, with his massive secret insecurity, and 2) Mrs. Ramsay turns out not to be all that great. We mean, she's still lovely and sympathetic, but she knows that James isn't going to get to the Lighthouse. And she regrets the fact that she disguised the truth from him ("She felt angry with Charles Tansley, with her husband, and with herself, for she had raised his hopes" [1.18.8]), but she still lied to him in the name of preserving his feelings.
In the end, while she's angry at Mr. Ramsay for oppressing James, Mrs. Ramsay does nothing to change his behavior. In fact, Mrs. Ramsay actively wishes that James would stay a child forever (1.10.10) because she loves him as a child. This works directly against James's desire to grow and replace his father. Similarly, Lily Briscoe is fully aware that Mrs. Ramsay is willing to care for Lily – but only on her own terms. She's not willing to go out on a limb for Lily's painting ("one could not take [Lily's] painting seriously" (1.3.7), thinks Mrs. Ramsay). And she still believes that Lily must marry William Bankes. Lily feels Mrs. Ramsay's pressure on her to be married and resents it, despite her affection for Mrs. Ramsay as a person.
In the midst of James Ramsay's efforts to get to the Lighthouse and Lily Briscoe's efforts to get recognition for her artwork, To the Lighthouse draws its focus away from the people of the novel. The second part of the novel experiments with the passage of time through focusing on the shifting, decaying form of the semi-abandoned house on the Isle of Skye, with limited interruptions for the deaths of Mrs. Ramsay, Prue Ramsay (she falls ill in childbirth), and Andrew Ramsay (he is killed in France by a mine during World War I).
These deaths must leave the structure of the Ramsay family forever changed (as, not to get too melodramatic, the intrusion of World War I left England forever changed – see how Virginia Woolf gets at massive movements of history through the lens of the everyday? Good stuff!). So this section of the novel provides a kind of climax for James and Lily: they're left in suspension (as are we, the readers), waiting to see what's going to happen to them now that Mr. Ramsay has lost the soothing, socializing influence of his wife. They were trying to find places for themselves in the Ramsay family as it was in the first section; now, they must work out what space there is for them in the Ramsay family as it will be in the last section.
The third part begins with Lily Briscoe asking, "What does it mean then, what can it all mean?" (3.1.1), and boy, we're right along with her. What does all of this mean? That's where the suspense comes in: we're waiting to see if there's going to be any purpose or conclusion given to the James Ramsay and Lily Briscoe story lines now that Mrs. Ramsay has died.
And we find out almost immediately that there is going to be some kind of continuation with the plot lines of Part One. James is finally getting his expedition to the Lighthouse, but this time, it's on his father's terms and he's being forced to go with his sister Cam. As for Lily Briscoe, she still feels the oppressive force of Mr. Ramsay that interfered with her painting so many years ago. And she, like James, is picking up where she left off:
She must escape somewhere, be alone somewhere. Suddenly [Lily] remembered [...] There had been a problem about a foreground of a picture. Move the tree to the middle, she had said. She had never finished that picture. She would paint that picture now. It had been knocking about in her mind all these years [...] She had borne it in her mind all these years. It seemed as if the solution had come to her: she knew now what she wanted to do. (3.1.7-8)
In other words, both James and Lily are picking up their quests again, but they're starting from different places. They must begin in other ways because the James and Lily – and indeed, the Ramsay family – of ten years ago have disappeared. As we read, we wonder if this new James will reach his Lighthouse and this new Lily will finish her picture, as neither succeeded in doing in Part One.
The suspense portion of the plot for both of these characters certainly covers most of Part Three. Both James himself and his sister Cam observe James's growing resentment of his father, as he chats anxiously with Macalister and continues to criticize and bully his children. This trip seems almost like an intensification of the strain between the two men, and between Cam, her father, and her brother that we saw in Part One. On Cam's part, she finds herself feeling drowned in the competition between James and Mr. Ramsay, seeking comfort in the dreams the steady rock of the boat inspires: "It was a hanging garden; it was a valley, full of birds, and flowers, and antelopes" (3.12.3). This echoes the lullaby that Mrs. Ramsay spoke to her when she was afraid of the boar's skull in Part One, the skull that Mrs. Ramsay wrapped in her shawl to cover it from view. Cam is capable of being soothed, of ignoring the ugly truths under things. As her father and James lock in silent struggle, Cam sits to the side, quietly stifling.
James becomes wearily resentful of Cam's unwillingness to take his side (much as his mother failed really to take his side over the Lighthouse thing in Part One?). So, between his father's bullying and James's resentment of a female family member, it's almost like old times. Meanwhile, Lily Briscoe is watching Mr. Ramsay's boat tacking towards the lighthouse, and as she paints, she considers her relationship to the Ramsay family. Once again, her painting is like a magnifying glass for her to use small subjects – a tree moved towards the middle of the canvas – as a jumping off point for larger explorations of past, present, art, and reality.
In Part Three, Chapter Twelve, Mr. Ramsay praises James Ramsay for his steering skills. At last, he acknowledges that James has talents in his own right, that he need not control every aspect of James's life.
James Ramsay and Mr. Ramsey share a moment of mutual understanding at the Lighthouse, witnessed by Cam: "[James] was so pleased that he was not going to let anyone share a grain of his pleasure. His father had praised him. They must think [James] was perfectly indifferent. But you've got it now, Cam thought" (3.12.15). Mr. Ramsay has at last given some of his power to the next generation. He will always be a domineering father, but he's brought up James to follow in his footsteps, and he is willing at last to let James take his place at the Lighthouse. We finally learn what James's quest to get to the Lighthouse really means: he is taking up the social and intellectual authority of the Man. (See "The Lighthouse" in "Symbols, Imagery, Allegory" for more.)
Lily Briscoe, for her part, is attempting to create a different heritage for herself. She's trying to make peace with the memory of Mrs. Ramsay, both her quiet bullying (why should Lily have married Mr. Bankes?) and her all-encompassing love (Lily learned a great deal about the importance of the little things in life from Mrs. Ramsay). Lily's peacemaking with the memory of Mrs. Briscoe gives her a way to solve her aesthetic problem of how she should be painting:
One wanted, [Lily] thought, dipping her brush deliberately, to be on a level with ordinary experience, to feel simply that’s a chair, that’s a table, and yet at the same time, It’s a miracle, it’s an ecstasy. The problem might be solved after all. Ah, but what had happened? Some wave of white went over the window pane. The air must have stirred some flounce in the room. Her heart leapt at her and seized her and tortured her. (3.11.21).
Lily gets the everyday from Mrs. Ramsay, but the "miracle," the "ecstasy" – that's all her own artistic aspiration. "The problem" that she's looking for, how to capture that miracle, is something that Mr. Ramsay is also, in a sense, seeking. He's got his theorem in Part One that he never finishes, but Lily's focus on the everyday gives her enough to work with that "the problem might be solved after all."
It's in this moment of realization that Lily understands that Mr. Ramsay has no authority over her. She is effectively outside the traditional family structure of the Ramsays. He has firmly established his heirs, James and Cam, who sail with him to the Lighthouse. Lily is free to do something different, to carve out an artistic legacy for herself.
Lily has come to realize that Mr. Ramsay doesn't have to bother her any more. She has solved with art what he attempts to solve with philosophy. Her willingness to look outside the ordered rationality of social and philosophical structures has given her true inspiration. She has broken free of the bonds of traditional class and gender roles to capture something more essential: a true moment of aesthetic revelation.
Following the denouement, we get a final chapter in Part Three. Lily Briscoe sees that Mr. Ramsay's boat must have arrived at the Lighthouse. It's at this moment, when she observes from afar Mr. Ramsay's greatest moment of family bonding, that Lily really gets the degree of perspective on the Ramsay family that she's been searching for all of these years. Lily and Mr. Carmichael (a successful poet) have both achieved an aesthetic resolution. They may not share the Ramsay family's social status, but their abilities to capture the essence of such scenes gives them intellectual and artistic security outside the conventions of marriage and family life. Lily has come to understand that all of the minor pressures of Mr. and Mrs. Ramsay on her fate have fallen away – which is perhaps why the Lighthouse (and all the social and family pressures that it represents) "had become almost invisible, had melted away into a blue haze" (3.13.1). Lily has solved the problem of the Lighthouse and how she can operate independently of it as a single woman artist: she has, at last, completed her painting.