Chicago is on the hook for $31.9 million next season, with the cap set at $54ish.
If Lebron/Bosh signs for $20 in his first season there, that leaves them $2-$3 under the cap, without an MLE or starting shooting guard.
If we (or anyone) sent them a package of Ray, Daniels and Sheed (for example) at a combined salary of $16.3 million they would have a starting shooting guard, some bench depth, and close to $7 million under the cap.
By the way, Deng just turned 25. Six months younger than Perk, 10 months older than Rondo, and an excellent defender.