The lighthouse is locked. You would need to find a key.
You will find the key into the lighthouse while doing other things.
Have you visited the club Blue Casket?
And you met Nick and Lola?
Did you talk to Nick at the High Roller's Lounge?
Then you probably got his cigarette case. He left it on the table.
Open the cigarette case.
If he doesn't leave his cigarette case, advance other puzzles.
That is the key into the lighthouse.