I don't always remember what a story is just by the title, but I have written over 200 stories. I don't believe I could remember them all by title no matter how I titled them. (Recent stuff I immediately recognise, as well as stuff that is in some way memorable to me, but for example, I got kudos on a five-or-so-year-old drabble the other day and had to click through to AO3 to see what fic it was.)
I use song lyrics for a lot of my titles, but I don't expect the reader to make a connection to the song. Not all readers are going to know the same songs, or recognise lyrics even if they do know the song, but also sometimes the rest of the song is irrelevant for what I want to get across (actually this is more likely the case than not). When I use lyrics for titles, all the meaning I want is contained in those words, so you don't have to know the song to see why I chose it; it should be obvious once you've read the fic.
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I use song lyrics for a lot of my titles, but I don't expect the reader to make a connection to the song. Not all readers are going to know the same songs, or recognise lyrics even if they do know the song, but also sometimes the rest of the song is irrelevant for what I want to get across (actually this is more likely the case than not). When I use lyrics for titles, all the meaning I want is contained in those words, so you don't have to know the song to see why I chose it; it should be obvious once you've read the fic.