"All the world-class players I've seen, they go into training every day, not complacent about their talent, not thinking they've made it and they're the best," Lee told liverpoolfc.tv.
"Every day they go in there determined to be the best - and importantly, to be even better.
"I played for over 10 years at Liverpool with some of the great players, people like Graeme Souness and Kenny Dalglish, and I've coached some of them too, and for me, all the world-class players have one thing in common - and that is their attitude.
"Of course he's got incredible ability. But it's not just about the ability, it's about the attitude too, and believe me, his has always been absolutely right.
"Personally, I don't think it serves any purpose to compare players over different eras because, for me, it's impossible. So it's not for me to say Gerrard is better or worse than Souness. But like Graeme and Kenny, he shares the same approach to the game.
"I saw him come through as a kid at the club, and the first memory I have of him is not of any one game where he suddenly stood out, but just of the talent he always had.
"From the start, you saw him around the place and he had a great effect on people, because he was a young lad who had the right attitude.
"Steven had that mentality, that steely determination to do his best and become better, and he still has that now. I don't know if he will get even better, but I can say he'll still be thinking about it now, even after 10 years, that he can still improve on what he has already achieved.
"That's what marks him out as up there with the great players."