Lee was sacked as Bolton manager last season before returning to Anfield as assistant manager to Rafael Benitez. Kevin Nolan says Lee's departure was a big loss for the Trotters and a boost to the Reds.
"I think it was always going to be a tough job to follow in Sam Allardyce's footsteps. Sammy tried it his way but I didn't think it worked at the time," said the Bolton captain.
"I'm sure he will learn from his mistakes if he goes into management again.
"What was our loss as a first-team coach and an assistant manager - and then as a manager - was Liverpool's gain.
"You can see how good a coach he is and I think that's one of the major reasons why Liverpool are where they are.
"I've not spoken to Sammy for a good while but it will be nice to see him.
"I'd like to get one over on him but I'll also wish him all the best because he's a great fella."