I don't think either PG is the right "type" for playing alongside of Lebron. Cleveland would be better off with someone who doesn't need the ball in their hands so much to be effective, but is also a solid spot up perimeter shooter, as well as a solid defensive player. Someone like Derrick Fisher in his prime.
Kyrie could be closer to that, simply because he shoots the ball far better than Rondo, but I think Rondo would actually be better for that team simply because he knows how to get teammates involved in the offense better. There is also the issue of Kyrie's mentality. He thinks score first, score second and score always. He also doesn't have the ability, at least not so far, to humble himself and defer to Lebron as he should be.
Regardless of whether or not Cleveland trades Kyrie for Rondo, which they won't and shouldn't, they probably would be best served by trading him for other needs.