Grayson was impressed with Lee following his first start of the season in the 4-2 defeat against Yorkshire rivals Leeds on Saturday.
"We asked Alan to do a specific job against Leeds and I thought he was effective, especially in the air," he told the Huddersfield Examiner. "It's a shame that we couldn't better utilise some of the balls he won.
"Alan's not only an experienced player, he also has bags of enthusiasm, and that rubs off on those around him.
"He's great at helping out the younger lads in the squad, both on and off the pitch, and while he might not start every game, he has a big role to play."
The 34-year-old forward could retain his place in the Terriers' first XI for this Saturday's clash with Bolton, who are managed by Lee's former Crystal Palace team-mate Dougie Freedman.