Lampard, one of the all-time greats for Chelsea and for the Three Lions, took on his first job as manager this week by penning a three-year contract at Pride Park.
Dawson, meanwhile, is now back at first club Forest - Derby's arch rivals - following 13 years at Tottenham Hotspur and Hull City, while also winning four caps for England.
"Frank Lampard, what a player! I played against him on many occasions. He scored goals. He was box to box. Wow, what a player," Dawson told the Nottingham Post.
"Those players are world class – to play at the highest level and win as many trophies as the likes of Frank Lampard, John Terry, Steven Gerrard, Rio Ferdinand did. Those players are of the era that I looked up to. To play against them, wow! And then to play with them in the England setup!
"He's gone into management. Obviously Derby is a big rival. It's his first management job, it's always hard. It's hard for young ex-players to get the opportunity. He's got the opportunity and it's one I'm sure he's excited about."
Forest and Derby, both currently in the Championship, contest the East Midlands derby and the Brian Clough Trophy, named after their former manager and currently held by the Rams.