The most important provision is that other teams must sign Butler for at least three seasons with no options. The Lakers therefore cannot sign Butler to a one-year contract and they can't even sign Butler to a deal with an opt-out after the second year like Dallas did with Chandler Parsons last summer.
Therefore -- assuming the Bulls exercise the Maximum Qualifying Offer and assuming they'll match any offer sheet -- the only real way Butler could leave Chicago and sign with L.A. in the near future is if he takes the one-year, $4.4 million tender from Chicago and becomes an unrestricted free agent in 2016. Butler would surely have multiple teams offering him a maximum contract then, and he'd have much more freedom to leave Chicago. That deal would also be worth millions more than it is now due to the salary cap's jump.