The secret to winning Luke over is not to rush... you need to wait at least two days between invitations so that he doesn't get suspicious. It also helps to talk to him on the phone, to create intimacy
As for the conversations, the clues to what to say are all on his profile on I.nstagram... remember that his page is constantly being updated, so it's good to keep checking.
If you lose patience, you can take a look at the walkthrough on the game's Patreon page. It's open to everyone
https://www.patreon.com/posts/walkthrough-luke-90544353
Thanks for your support! It means a lot!