James Ramsay is the youngest of the Ramsay family's eight children. He starts out the novel as a six-year-old and ends it as a melancholy, sullen sixteen-year-old. James's entire character revolves around his desire to go to the Lighthouse: in Part One, he desperately wants to go but will not be allowed, and in the Part Three, his father makes him to sail there almost against his will. James's obsession makes it obvious that this Lighthouse isn't just a lighthouse; it's in the title, so it's got to have huge symbolic significance. Want to go and then refusing to go to the Lighthouse becomes one tool to show the reader James's shifting, difficult relationship with his father.
James is caught between his profound bond with his mother and his fiercely competitive relationship with his father. Even at six, he's filled with apparent loathing for Mr. Ramsay and the place that he occupies in Mrs. Ramsay's life. And James's fixation on Mrs. Ramsay is by no means one-sided; Mrs. Ramsay wishes that James (and his sister, Cam) would never grow up: "She would have liked to keep for ever just as they were, demons of wickedness, angels of delight, never to see them grow up into long-legged monsters" (1.10.10). Mrs. Ramsay, as mother of eight, derives much of her identity from being a Mother (with a capital M); her intense relationship with James (and, to a lesser extent, Cam) keeps that maternal identity alive.
Of course, the problem with maintaining Mrs. Ramsay as the ultimate Mother is that James doesn't just want to be her son. He kind of wants to be his dad. He fantasizes about plunging a knife into Mr. Ramsay's heart – and because we have no evidence that James is actually a psychopath, we have to figure that this is symbolic of a more general desire to replace his dad, to prevent his father from interrupting James's special tie to Mrs. Ramsay. And Mrs. Ramsay is, in a subtle way, complicit in this competition between these two men in her life:
"Perhaps you will wake up and find the sun shining and the birds singing," [Mrs. Ramsay] said compassionately, soothing the little boy's hair, for her husband, with his caustic saying that it would not be fine, had dashed his spirits she could see. This going to the Lighthouse was a passion of [James's], she saw. (1.3.1)
Mrs. Ramsay knows that James, in wanting to go to the Lighthouse, is thirsting after independence from his father's control. Mr. Ramsay's caustic (or, in other words, harsh) refusal is squashing little James's spirit. Mrs. Ramsay sees the power struggle going on here, and does her best to soften the pain on both sides, but in the end, she's as invested as Mr. Ramsay in keeping things as they are. So she's mad at Mr. Ramsay for being mean to James, but she also recognizes the necessity – after all, if the weather is bad, they can't sail to the Lighthouse. From Mrs. Ramsay's perspective, it's the natural order of things that Mr. Ramsay should be able to make James knuckle under. After all, he's the father of the household. (For more on how the Lighthouse works as a symbol of traditional family structures, check out "The Lighthouse" in the "Symbols, Imagery, Allegory" section.)
Anyway, all of this kind of changes in Part Three, when Mrs. Ramsay has died and the Ramsay family is returning, for the first time in ten years, to that old house on the Isle of Skye. The love triangle is gone: there's no more Mrs. Ramsay for James and Mr. Ramsay to compete over. So, why, after all this time, does Mr. Ramsay insist that the family sail to the Lighthouse? Well, he's got a figurative torch to pass to the next generation. He compels James and Cam to accompany him, and in the process, there's a profound shift of power.
James starts out the trip all, "Resist him. Fight him [...] For [we] must fight tyranny to the death" (3.4.9). But the thing about tyranny is that it's all very well to fight it when you're one of the oppressed. It's a lot more seductive when you get to be tyrant. And the thing that is perhaps going on in this final voyage is that Mr. Ramsay is exerting the last of his control over the family to pass on his authority to his children – and especially, to James. Consider the moment when they finally arrive at the Lighthouse and James sees: "So it was like that [...] the Lighthouse one had seen across the bay all these years; it was a stark tower on a bare rock. It satisfied him. It confirmed some obscure feeling of his about his own character" (3.12.3, our italics).
What James finds in the Lighthouse is confirmation of his own character, of the character that he's inheriting from his father, who also loves the Lighthouse. The sudden doubling between James and Mr. Ramsay is underscored at the end of this paragraph, when James reflects, "They shared that knowledge. 'We are driving before a gale – we must sink,' he began saying to himself, half aloud, exactly as his father said it" (3.12.3). After all of his sullen resistance, James has been drawn in at last to the patriarchal power he's desired since he was six.
What "that knowledge" is, we the readers do not know. It is something ineffable shared between James and Mr. Ramsay, something that Cam, the sister, witnesses but can't join in. "But you've got it now" (3.12.15), Cam thinks, recognizing that James has finally inherited from Mr. Ramsay the praise that he has always wanted.
The thing about the Lighthouse, as we talk about in the "The Lighthouse" section of "Symbols, Imagery, Allegory," is that it's a symbol of both permanence and transience. The foundation of the family remains intact, but the man who fill the position of Head of the Family must change over time. James's final arrival at the lighthouse represents a shift of power in the Ramsay family. James has finally gotten what he wanted all those years (and pages) ago in Part One: James gets to be his dad.