more likely you need to train lin for the story progression. the list can be seen near the time forward option and located as "info".
you have to increase lins submissive traits in the dungeon. the event automatically trigers after a bit of story progression while you enter the dungeon.
Most of the traits are pretty obvious how to get them. For comdump = cum inside her more times. cumslut = cum on her more times. paizuri star = titty fuck her more times. you get it.
