What do we gain by playing Lee in garbage time? Nothing. What could we potentially lose? A trade for a star.
No one will be trading for David Lee because they want David Lee to play. In a trade for a star, he would be trade ballast needed to match salaries and you don't lose that if he gets injured.
I think Lee has some value for a bad team where he can average 16 points and 8 rebounds per game as a starter and let you bring along a prized rookie slowly without forcing him into the role of primary scorer on a team with no other offensive threats, so the ideal trade target is a team with young pieces and a star who is too old to go through a full rebuild.
If Lee could average 16 and 8 on any team, he would have started every game for us. The problem is that every time he even tried to take enough shots to score 16 points, it was an unmitigated disaster. The dude is cooked.