The most common and most likely answer to this crossword clue is the 6 letter word STARRY
I've seen this crossword clue in Financial Times
S
T
A
R
R
Y
More clues leading to the result STARRY
- Thus Vincent’s night visit, entertaining bishop
- Terribly artsy Romeo with many famous actors
- Small wait for such a clear sky
- Small wait? I’d sounded naively idealistic
- Bright in South — linger on
- Street supported by vulgar Cockney like Hollywood Boulevard?
- “The — welkin cover thou anon / With drooping fog as black as Acheron”
- Describing certain nights as a celebrity?
- Stellar sons dawdle
- Not showing head, badger below street lit at night
Buddy explains!

The straight part
We know that "lit at night" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case lit at night = starry.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does STARRY mean?
STARRY adjective- Having stars visible.
- Resembling or shaped like a star.
- Full of stars or celebrities; star-studded.