"I will take care of it later," Howard said.
Howard was limited to 11 points on 4-for-8 shooting in the Lakers' 109-103 loss to a Stephen Curry-inspired Warriors team.
But it was Lee who stirred Howard's ire. During the second quarter, Howard was whistled for a technical foul on a play in which his lip was cut when he was smacked in the face by a Lee elbow, shortly before the Lakers entered the locker room with a 63-40 halftime deficit.
"He got away with a shot," Howard said. "I will remember this game. I will remember that shot. He said he wasn't trying to do it. You can look at the play and see it for yourself. I will take care of it later."
Howard, who required three stitches for the cut, will have a bit of a wait. The Lakers host the Warriors two weeks from Friday, on April 12, in the third-to-last regular-season game for both teams.
Curry scored 25 points and had 10 assists two nights after sustaining a sprained ankle. The Lakers also struggled to contain Lee, who added 23 points and 12 rebounds as the Warriors improved to 41-31.
With the loss, the Lakers dropped to 36-35 and hold only a one-game lead over the Jazz for the eighth and final playoff spot.
"We are the better basketball team," Warriors coach Mark Jackson said. "They are in the rearview mirror and I have not checked it and I will not."
The frustration for the Lakers was apparent to end the first half. First, Metta World Peace jawed at Lee, then awkwardly patted the All-Star forward's head once officials intervened.
A few minutes later, Howard picked up the technical foul while exchanging words with Lee and an official after he was called for a foul on Lee's layup.
"We made a statement in that first half," Jackson said.
Information from The Associated Press was used in this report.