The Lute is in the watchtower on south_east of town. ( Go there at midnight to avoid guard)
SPOILER
You should get 1 key from the guard (who is sleeping) - you have to steal it from him
2. You open the second gate using the switch on the first ground floor (red one).
3. Last gate - you need to approach the jug on the right, get past the guards and open the chests.
PS. Sorry for late, I was watching arifureta.
you're welcome; anyways, bad news: did what I said and tried an older save file, only to run into the exact same problem when I got to the tower later on, I.e. I'm not entirely sure what's going on here, but I'm sorry to say that it's entirely possible that there might still be some bugs that are still in the game at this point in time :|