The excellent blog Ephemeral New York has a post on Brooklyn Heights’ perhaps most charmingly named thouroughfare. It quotes an 1894 New York Times article:
The oldest residents can remember a time when there was a cool and shady path leading down “Lover’s Lane,” where plump, rosy-cheeked Dutch maidens, with their sweethearts, meandered on summer evenings out through the turnstile and down the grassy bank to the water’s edge.
Wildnewyork, author of Ephemeral New York, adds:
I wonder if the name may have been reinforced by the presence of the Brooklyn Collegiate Institute for Young Ladies, an early 19th century finishing school located on what is now called College Place, a tiny lane that intersects Love Lane.
Perhaps eligible Brooklyn bachelors took romantic walks with some of the students here, making the Love Lane name really stick.