Derby will take on Championship rivals Reading in the fifth round of the competition at the iPro Stadium on Saturday.
The Rams will head into the tie as favourites, and former Liverpool defender Lawrenson backs Steve McClaren’s side to win it 2-0.
“Derby are going for automatic promotion to the Premier League but I think Rams boss Steve McClaren will see the FA Cup as a chance to keep their good run going rather than a distraction,” the 57-year-old wrote on BBC Sport.
“Reading have spent most of the season in the bottom half of the Championship table but I don't see them as being in danger of going down.
“The Royals are not going to reach the quarter-finals either, though. From what I have seen of them, Derby are the best all-round team in that division.”
Do Reading have a chance?
As Lawrenson points out, Derby are having a very good season in the Championship and are arguably the best team in the division.
The Rams are currently third in the table with 58 points from 30 matches, just a point behind leaders Middlesbrough.
Playing at home will give Derby an advantage against Reading, who appear to be safe in mid-table in the Championship.
However, one suspects that manager Steve Clarke will want his Reading players to step up their game and go for the win at Derby.
The Reading players will certainly want to give their fans something to cheer about on Saturday.