To the Lighthouse ends with Lily Briscoe having a revelation about her own work. She has seen from a distance that Mr. Ramsay has arrived at the Lighthouse, his children James and Cam in tow (for more on the significance of this story line, check out both our "Classic Plot Analysis" and our look at James Ramsay's "Character Analysis"). This sums up not only the achievement of Lily Briscoe's artistic project, but also of the project of To the Lighthouse as a whole.
The third part of To the Lighthouse shows Lily Briscoe picking up a painting that she had worked on throughout the beginning of the novel, which she never finished. Under the slightly discouraging influence of Mrs. Ramsay (who wants Lily to marry) and the actively oppressive influence of Charles Tansley, Lily never manages to find a way to capture what she's trying to say about life in her art.
The project of her second effort to paint is to reconcile "Mr. Ramsay," who, at this point, is a kind of shorthand for the pressures of masculine society, and her painting, which is experimental and private for Lily. And the way she reconciles these two opposites is to work through her memories of Mrs. Ramsay, who managed to live with Mr. Ramsay for years while raising children and doing good. Sure, Mrs. Ramsay may not have been perfect, and in many ways Lily has to overcome her moderating influence, but her pleasure in the everyday gives Lily the tools she needs to find a new way of painting outside of the influence of Mr. Ramsay and his like.
So, to the final section: as Lily paints, she manages to use her artwork to gain perspective on Mr. Ramsay and everything he stands for. She contains him and sees him for what he's worth. And in the moment that Mr. Ramsay reaches the Lighthouse (thus, as we the readers know, reconciling with his son), Lily sees that Mr. Ramsay truly has no power over her modes of artistic production. She can paint whatever she likes, however she likes, because she no longer feels the weight of the social and gender hierarchies that Mr. Ramsay once represented to her.
Indeed, this power that Mr. Ramsay once represented isn't only something Lily has stopped acknowledging. It's also something that Mr. Ramsay himself has let go. Lily sees that "He must have reached it" (3.13.1), that Mr. Ramsay has finally made his own peace with all of the intellectual burdens he's been fighting all of his life. And in that moment when Mr. Ramsay stops fighting the world, the Lighthouse itself seems almost to disappear: "For the Lighthouse had become almost invisible, had melted away into a blue blaze" (3.13.1).
Lily, with fellow artist Mr. Carmichael as a witness, has finally found an answer to her artistic problem of how she can paint, as a woman, without competing with the intellectual enterprises of tyrants like Mr. Ramsay. And her triumph is two-fold: not only does she find her own artistic confidence, but she also has come to terms with her past and present with the Ramsay family, a past dominated by Mrs. Ramsay and a present in competition with Mr. Ramsay. As Mr. Ramsay surrenders some of his own authority to his son, he becomes less of a direct threat to Lily and her artistic development. At last, Lily has been allowed to "have her vision."