Houston has lost three straight to drop to 1-3 since coach Kevin McHale was fired and replaced by J.B. Bickerstaff.
The Grizzlies led for most of the game despite playing without Zach Randolph, who missed his fourth straight game with soreness in his right knee.
Lee made the first points of the fourth quarter for Memphis with about 9 minutes left. It was the first of six straight points for Lee, a former Rocket, that pushed the lead to 88-79.
James Harden had 40 points for the Rockets. They are 5-10 overall.