I see no reason for David Lee to play at all if he isn't going to contribute significantly more than he is doing at this point. His defense is terrible. Worst on the team. Offensively, he has clearly lost a fair bit of quickness and he was slow for a PF even before this. No lift. Struggling to finish against length around the basket. Reluctant to shoot the jumper. Olynyk, Sully and Jerebko all provide more shooting. Olynyk and Sully comparable or better passing. Jerebko more quickness and movement. All 3 are out-working Lee on defense.
I think David Lee should be used almost exclusively as a center at this point in his career. He doesn't have the quickness / overall athleticism required to start at the PF position anymore. His skill level as a high post offensive center still has some value. Unfortunately, Olynyk offers the same thing with an even higher skill level so Lee doesn't offer the roster much at the moment.