Whoever has the higher goodwill when you play that chapter will speak up first.

The attempts refresh once a day. For the best use, give the character a gift that 1) matches their two likes and 2) has more gift icons. Tap and hold a gift to read its description, traits, and a gift scale (from one gift two five gift icons). I've unlocked all 105 combinations for gifts, and the best gift too Boost Lafayette's friendship is the Magic Carpet made with 1 fabric and 1 arcane essence.

Hope this helps!