A young man with no past, wakes up in a town where there's no future and everything's grey, meet an old man tells him he will never go back to his time unless he marry the only lady in town, who is eccentric.

Hello, this sounds like the beginning of the movie. In a logline you should outline the plot. What happens? What problems does the main characters has to face? What does “where there’s no future” means? Why an old lady can help him and how? Everything should be clear in a good logline.

Something like:
“When a teenage amnesiac wakes up in a town where everything is sad and grey, the only way to return to his world is to seduce an eccentric old lady who has the power to send him back”.
(You can do better than this)

Hope that helps.