Why was Proust searching for "lost time?"

“Lost time” has a double meaning in In Search of Lost Time. On the one hand, as already mentioned above, it refers to time lost in the sense that time is constantly passing us by, and it is difficult to regain, or recapture these moments from our past in full. For Proust, to truly recapture a moment means not only intellectually remembering it, but remembering what it felt like, as is the case in the famous “petite madeleine” scene.
The other sense of “lost time” pertains not to moments the narrator wishes to recapture, but to the “quest” of the novel, which is the narrator’s quest to find his true vocation. After hearing Vinteuil’s Sonata, the narrator has the epiphany that art may contain more truth than life: whereas in life, social convention may prevent people from getting to know the innermost selves of others, in art, the viewer or listener sees or hears through the perspective of another - the artist. Art may capture the inner soul, or “essence,” of the artist. The themes and motifs in Vinteuil’s famous Sonata are, for instance, characterized as “fairies” which are the manifestation of Vinteuil’s inner world. The narrator is not as interested in factual truths as he was in psychological truths, and was particularly fascinated with the possibility of coming to know the innermost soul of another person. Art thus carries more “truth” than life for him, a realization which brings the narrator to understand that his time as a socialite has been time lost in the sense that it has been time wasted: his true vocation is to write. In the costume-ball scene which comes at the very end, the narrator, seeing his aged friends, understands that he does not have any more time to lose and must begin to write.
“Lost time” thus refers both to the fleeting nature of time, and also to the time the narrator has lost leading up to his epiphany that his life’s purpose is to write. By writing, the narrator will both be able to capture and convey time past to his readers, as well as live the rest of his life with purpose.

Marcel Proust was such a gifted writer that he was able to make millions of readers believe in a false premise. The whole of his enormous multi-volume novel, beginning with Swann's Way, is motivated by the narrator's supposed urgent desire to recapture lost time before he dies. He is under time pressure because he is sick and growing old. This would be a thrilling experience--if anyone were able to do it. It would be like time travel. But it was invented to give the protagonist/narrator a motivation with which the reader could identify, and it was simply not true. Proust was writing a memoir. He did not "capture" anything he wrote in all of the volumes. He either relied on his conscious memory or on pure fiction. The petite madeleine dipped in camomile tea was--essentially--a gimmick. Proust's ability to resurrect the past was probably no better than our own. His book is essentially a memoir tailored to appear to be the story of a quest. In the last volume, Le Temps Retrouve (Time Regained) he claims to have succeeded in his quest, but the conclusion is somewhat disappointing because the characters have all grown old. The story about Swann's love for Odette could not be something the narrator remembered. How could he be remembering such tiny subjective details about what happened to somebody else? It is pretty obviously the narrator's own experience attributed to Charles Swann and the narrator's own feelings he is describing. Proust was involved in many love affairs with young boys, not young girls (in flower). Edmund White explains this in a short, interesting book called Marcel Proust. Proust changed the boys to girls in his story because it was illegal and dangerous to write about homosexual activities in the first person. A French author could write that somebody else had a homosexual liaison, writing in the third person, but not that he had one himself, writing in the first person--which could be construed as a confession. This explains why so many of the "girls" the narrator knew, including Albertine, had so many homosexual relationships with other girls. These were really boys with boys. Proust could not hold on to his boyfriends in spite of his money, culture, and social status. He was always losing them to other boys or to older men. Swann's love for Odette may have been a disguised tale of Proust's love for an unknown young lad. We cannot take anything at face value. Remembrance of Things Past is a work of fiction, a brilliant, subtle and sensitive work.