And the question of Lawes' indiscipline reared its ugly head at the World Cup when he was found guilty of striking Argentine Mario Ledesma, missing the group games with Romania and Georgia through a two-week suspension.
But former Red Rose lock Grewcock, who was no stranger to controversy during his playing days before moving to become academy director of Bath this season, insists the giant second-rower shouldn't listen to anything being said regarding his temperament.
"Courtney is a very good player and I don't buy into what is being said about him and his temperament," said Grewcock, a member of England's 2003 World Cup winning squad.
"He is a very good and very strong second-rower who does what he has to do in a very physical position to make his presence felt.
"I think that all this talk about his temperament has been blown out of all proportion and I would advise him to not listen to any of it, although he knows that himself I am sure.
"The important thing for him is that he is happy with how he is playing and as long as his coaches and teammates are happy, and I am sure they are, then there isn't a problem.
"Plenty of people will have opinions but his character doesn't seem like the type of guy who will let that bother him and it shouldn't because he has nothing to worry about."
Lawes and the rest of the England team returned from New Zealand with serious questions to be answered, Martin Johnson, who led the side to last season's RBS 6 Nations crown, having already fallen on his sword following poor displays both on and off the field.
And as the search for a new coach begins by the RFU, Grewcock believes that the one thing the new man must not change is Lawes' name on every teamsheet.
"For me, Courtney is the best lock England have and is by some way," he added.
"He broke in and has done a very good job and looks to have made that second row position his own in the face of some stiff competition.
"A lot will happen with the England side for sure but the one thing the new coach can be sure of is that he has a ready made lock in Courtney ready and waiting and if there are going to be changes I would make sure Courtney isn't one of them."
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