How do I unlock the dungeon? It says spend time with Luce, but I can't find an option to "spend time with her" only to have sex with her
Depends where in Luce's storyline you are, but realistically, it's probably another character that might be slowing things down. Once everyone has a certain amount of storyline done, it should unlock naturally. The servant's quarters, barracks, will push Luce's storyline, usually. If you tell me exactly what it says in Luce's character logs I could tell you more precisely.