The set-up for the quest is that life has become "oppressive and intolerable," and the hero "can only rectify matters by making a long, difficult journey." So Christopher Booker tells us. And frankly, we think James Ramsay would mostly agree with this assessment: life in his father's household has gotten oppressive. And if only he could get to the Lighthouse, reasons six-year old James, life would be much better. Maybe he'd even be able to make time with his mom.
However, this initial call is thwarted right from the start: James is still subject to the dictates of his father, who won't let him go. So this call for a journey won't be answered until after his mother has died and his father has begun to think of passing on his power over the Ramsay family at the beginning Part Three.
As for Lily Briscoe, she's laboring under a lot of social judgment: she's getting older, she's not very attractive, and she has the unusual aspiration (for a woman in the late Victorian era) of becoming a painter. So the only way that she perceives that she can defend herself from Mrs. Ramsay's well-meaning interference to get her married and Mr. Ramsay's less-well-meaning dismissal of her painting is to find an artistic identity for herself that would be separate from her identity as a woman in Victorian England.
Just like James Ramsay, though, Lily feels this call throughout the first section of the book, but cannot truly act on it until Part Three, when she has had some time and distance away to reflect on the bewitching, influential figure of Mrs. Ramsay.
Both James and Lily embark on their journeys at the beginning of Part Three (aptly named "The Lighthouse"). James encounters "monsters" (apparently necessary in any quest narrative) in the form of his father and Macalister (the boat captain), both of whom seem to be speaking the same kind of traditional male-bonding language without paying too much heed to James – who's also wants to be recognized as a man. The ordeal that James is undergoing here is the increasing tyranny and anxiety of his dad, who's getting more and more difficult for James to deal with the closer they get to the Lighthouse.
Lily, for her part, is having to do battle with the monsters of the past: as she paints the scene before her, she recalls the strain and hostility she sometimes felt with her beloved Mrs. Ramsay. She remembers the subtle, quiet ways that Mrs. Ramsay attempted to compel Lily to act against Lily's own wishes (Mrs. Ramsay's matchmaking attempts with Mr. Bankes spring to mind as an example). Lily struggles to capture something of Mrs. Ramsay's beauty and poise without being personally overcome by Mrs. Ramsay's love for tradition.
Arrival and Frustration
Booker informs us that, once the hero arrives within sight of his goal, he realizes that there's more left to his road than he thought. And James definitely feels the frustration that Booker describes. James is instructed to steer this wretched boat that's going to the Lighthouse, so you'd think that his hard work would be acknowledged by his dad. Even old Macalister says that James has manned the tiller like a real sailor. So why can't his dad just once acknowledge that James is doing a good job?
Lily, meanwhile, is caught up in her memories of Mrs. Ramsay. She remembers that Mrs. Ramsay, like Lily herself, attempted to capture moments in the flow of time. These moments, for Mrs. Ramsay, were social or familial; Lily, of course, paints her still moments on canvas. But the solution for the problem that she has presented to herself, the opposing forces she has set up between Mr. Ramsay and the painting, remains unsolved: "it evaded her now when she thought of her picture. Phrases came. Visions came" (3.11.6) — but never precisely the right visions.
The Final Ordeals
We have to say, we feel that the frustration James and Lily experience on their respective quests is their final ordeal. So, this additional stage doesn't apply.
Both James and Lily get to where they want to go in the end. James makes some kind of peace with his father, and James decides to take his place at the Lighthouse as a Man. Tickled by his father's praises, James takes up his father's mannerisms and ways of thinking. Mr. Ramsay and James have formed a direct intellectual line from father to son.
Lily has also succeeded in creating, from her memories of Mrs. Ramsay, a new, feminine artistic trajectory, in which she uses the everyday as a lens to capture larger truths (or "visions") about human life.