They are, as noted, complete synonyms.
They are both the past tense of light, one treating it as a weak verb and one as a strong. While lighted is the older, lit has been around since the 1500s, and both have lasted some time.
Hemmingway was writing in 1933, and it appears that then well-lighted was considerably more commonly used than well-lit.
Not as common as "well lighted", though he uses that too in the story; choosing to hyphenate when using it as a compound adjective modifying place, and not to when using it as a compound adjective following is; "It is well lighted."
That said though, even if lit were more common at the time, lighted would serve better there. Look at how often light is repeated throughout the story, often close to rhyming words bright and night; this last repeated several times too. Since lighted keeps with that repetition of /aɪt/ sounds more than lit would, it has a poetic benefit in this story that doesn't apply to most cases where one would choose between them.