Yet through it all, the 6-foot-2, 236-pound Lee has a huge smile plastered on his face.
"It's such a great feeling," he said when asked about donning a Dallas uniform for the first time. "It's a dream come true, just coming to an organization like this."
While Lee begins learning the basics of the Dallas defense, he is getting what amounts to private tutoring sessions with linebackers coach Reggie Herring, and then runs drills with the defensive linemen.
"I have a lot to learn," he said, "but that's the fun part about football. I just want to learn as much as possible."
Lee said he expects that learning process to accelerate once he begins working with the team's veterans at OTAs and the full-team mini-camp in June.
"Some of those guys are 13 years ahead of us," he said, presumably referring to starter Keith Brooking. "They have a lot of talent, but they have a lot of experience, too. I'll learn so much from those guys."
Lee squirmed when asked if he sees himself as the eventual heir apparent for Brooking, who will turn 35 in October.
"I feel I've got a lot of work to do to be mentioned that way," he said. "I mean, I feel I can play at a high level, but to look at him … that would be a dream come true to play at that level."
The Cowboys clearly thought Lee could play at a high level, ranking him as a player worth taking somewhere in the middle of the first round. Such a lofty pre-draft evaluation also showed the team isn't concerned about the health of Lee's knees.
He missed the 2008 season at Penn State after blowing out his right knee; at mini-camp, he is wearing a brace over his left knee, which he sprained in 2009, causing him to miss a few games in his senior season (Lee said the brace is merely a protective precaution now).
"I hadn't realized that," he said. "I knew they liked me as a football player, and it's nice to know they know I can play, that I can come back from injuries and that I can play through injuries."
As giddy as Lee is to be in the NFL, he seems that the fact that it was the Cowboys who drafted him means a conversion of sorts — for himself, and for his family and friends back home. Whereas many rookies arrive for their first mini-camp and claim to have grown up rooting for the Cowboys, Lee admits that's not the case when living in the home of the Steelers.
"As soon as I got the call from (Dallas owner Jerry) Jones, we went out and bought all the Dallas stuff we could find … which wasn't a lot," he said, laughing. "I've already had a lot of people up there say, ‘I'm going to root for you, but I'm not going to root for the team.' And that's OK.
"I looked at my helmet, and I couldn't believe it had the star on it. I'm joining one of the greatest franchises in the world. This is a dream come true."