Basically, what should happen is.
1. You meet the mayor, to discuss saving Lily.
2. Then sleep and then tell Lily the next day you'll train her.
3. After she agrees, you try training her/helping her study but you aren't smart enough.
4. You go find Bront during the morning to help you study.
5. Then you should go back and train/help Lily study again
6. You then train Lily's love and submission to level 5 and then sleep.
It should work since there's really no room for change here, but if somethings gone wrong, maybe make a new save file and see.