Friends, let me draw your attention to that little-used S&T option: The non-guaranteed deal.
We want to keep KG, Perk, and Sheed (perhaps), and like BBD sometimes, hate him sometimes, but generally agree that better players exist in the universe. His deal is reasonable at 3 million, which isn't enough to work a deal for Lee.
Enter Scal.
Scal gets signed to a non-guaranteed deal and is paired with BBD and next year's 1st round pick in exchange for Lee.
Presto: the Knicks get a cheaper but competent (mostly) replacement in BBDavis plus a 1st round pick, get to immediately dump Scal, who makes $250K or so for his signature, and we get Lee. It's not a great deal for NY, but it ain't bad. Scal becomes a FA, available for the minimum if anyone wants him to fill out a roster.
We lose BBD, but Lee becomes our 4th big, giving us, undoubtedly, the best four-big rotation, perhaps, ever, and KG's replacement.