What are beautiful motive quest's prerequisites?
This is pretty much from memory so I might have forgotten a bit here and there but this should be your path
First off you should obviously be kind to Lindsey and choose answers/options that make her happy
Once you have completed the "Tour de School" intro quest chain (choosing the Isabelle MQL) go quest Lindsey to start the "Fully Booked" quest.
When that is done you should be able to approach and Quest her again then going from the Entrance Hall up the stairs to the First Hall starting the "Nothing Wrong With Me" quest.
During that quest choose to help Lindsey instead of following up with Maxine's theory.
Then it should be "Dead Girl's Score" by talking to (or maybe questing) Lindsey in the Gym. You'll have to fix the piano like you would for the "Twisted Desire" and "Chops and Nocs" quests.
I believe you must then quest Isabelle while she is in the Entrance Hall to start the "Stolen Hearts" quest. (While not necessary it would probably be wise to tell Isabelle that Kate took the chocolates.)
At that point you should be able to go into the Gym one more time and quest Lindsey to start "A Beautiful Motive". (For best results turn down painting someone naked)
Hope this was helpful, good luck!