Now, we all know that Mike Brown left John Kuester with a lot of freedom in creating the Cleveland offense. Regardless, Mike Brown was the head coach at the time and the team would not run anything that did not have his consent.
Assuming that Mike Brown will be implementing an offensive scheme similar to that, we have to look at what made that offense work. There are two reasons as to why that Cleveland offense worked:
1) Cleveland was absolutely laden with shooters
2) LeBron was willing to pass to the open shooter
How does this translate for the Lakers? Well, they obviously need shooters on their team. I know that FIsher, Artest, Blake, Brown and Barnes are all capable shooters, but they also enjoy driving to the basket—sometimes doing it more than actually shooting the three-point shot.
When you have behemoths underneath the basket, you need a number of shooters to offset the other team trying to clog the middle.
The Lakers need a player or two that really rely on the three-point shot/jumpers as their main source of offense. Players in that mold that come to mind are Eddie House, James Posey, JJ Redick, etc. Doing so keeps the middle a little less crowded, making it easier for players to slash and post up.
Now, many call Kobe a ball-hog, and granted he does play like one from time to time, however, I've noticed that Kobe really plays like that when his teammates aren't producing. Passing the ball to teammates is a sign of trust. I think we can all agree that if we were on the same level as Kobe in terms of basketball skills, we wouldn't pass the ball to someone who you know or can't trust to hit an open shot.
With all that, the Lakers need to find a player or two that can shoot the deep shot AND make it on a consistent basis. Remember, trust is earned. If things go that way, the offense will work itself out.