Rozier & Doncic
I think Terry would work well with Luka. Rozier needs the ball in his hands some of the time. Not all the time. Rozier will be at his best alongside a playmaking 2/3/4. A player who allows Rozier to be more of a secondary ball-handler in the halfcourt. Rozier isn't a good enough playmaker to be the main creator for any team. He is a scoring combo guard. Not a real PG.
Rozier is willing passer. Not an overly intelligent passer and certainly not a creative passer but he is a willing passer. I think he is getting too much criticism for non-passing which I do not think is accurate. Rozier makes 40 passes a game in 22mpg vs Kyrie at 50 passes in 32 minutes.
Rozier won't create much for his teammates but he will share the ball and give others opportunities to create for themselves.
Rozier & Carlisle
I agree with everyone else who said this pairing is a problem. Rozier is too wild / erratic for Carlisle. Carlisle likes controlled guards. I think he'd have a tough time dealing with Rozier.
At least Rozier doesn't turn over the ball. That is Carlisle's biggest no-no on offense. Still, hard to see those two working out.