Regarding the fear of Kyrie to get bored and also the troubling interaction with Lue, I think Brad Stevens helps a lot with both.
Stevens being a good coach is too often thrown around as a cure-all for any potential problems but I think, in this case, his style is perfectly suited to dealing with Kyrie's issues. Stevens is the type of coach who can bring players into the fold and make them feel like they're part of the process. He dictates principles, but not plays and not style. And he knows that someone like Kyrie needs to be involved and that Kyrie is intelligent enough to make him a sort of partner as a team leader.
I think that same thing helps with the fear of Kyrie getting bored. He got bored in Cleveland when everything was about Lebron and all he was being asked to do was score. By being asked to do more for the Celtics (in terms of leadership both on and off the court) he's less likely to get bored.
And I think Stevens is not the kind of coach to go to a player and say something as simplistic as "play faster." I'm no NBA coach but that type of direction seems like it wouldn't be all that effective for anyone, especially someone who thinks of himself as an intellectual like Kyrie. A good coach knows that different people are reached in different ways. I think Stevens knows that and Kyrie's own admission about that exchange is encouraging.