If Melo joins the Bulls, it doesn't matter where Lebron goes in the East. Bulls will be the favorites. Kyrie-Lebron-Wiggins is not even as good as Miami was last year (Kyrie is getting overrated -- he ran a team that ended up with the #1 pick last year), and a Melo-led Bulls team has everything that the 2013 Bulls were missing even if Rose doesn't return to superstardom. They would give Miami fits, and they'd beat that Cleveland arrangement too.
That being said I doubt Melo is going to Chicago. He probably ends up back in NY with Gasol and the Knicks grab the 8 seed for the next couple seasons.
Bulls will most likely grab Mirotic and a couple solid role players who can start. Maybe Stephenson, maybe Shawn Marion, maybe they make a run at Gasol, maybe Ramon Sessions becomes the latest backup guard to flourish there. They will be a deep team, if Rose is healthy they will win the Central without much challenge from Indiana, they will win 55 games, and they very well could beat wherever Lebron ends up because they will have some pretty sick depth and shooters off the bench.