The outspoken cricket critic and former international coach has expressed surprise that Lyon was anointed as the player to lead Australia's celebratory team song at the end of a winning Test.
Lawson, 55, says the appointment to replace just retired star Mike Hussey as team choir master should have gone to a player with greater security on his Test spot.
"That normally goes to someone you think is going to be in the team every week, speaking as an ex-Test player," Lawson said on Sydney morning radio.
"He's getting a lot of wickets in the outfield and not too many up close.
"He didn't have a lot of luck this (Sydney) Test match. He had a couple of nicks that hit the 'keeper on the gloves and in the leg and things like that.
"He could have got a couple more."
Lawson analysed the beleaguered Lyon's repetitive off-spin and declared that the finger spinner has limited variety.
Lyon, 25, took 12 wickets at an average of 40 in three Tests against South Africa late last year and then seven wickets at a cost of 43.8 in another three clashes with Sri Lanka.
He is constantly under fire for a lack of significant impact late into Test matches when pitches are worn and generally favourable to spinners, as well as not taking enough top-order batting opponents.
Lyon has taken 61 wickets from his 19 Tests at an average of 32.1 since making his debut against Sri Lanka at Galle in September of 2011.
"I think he is bowling the same ball too often," Lawson said.
"He gets into this one rhythm, he just goes along and just bowls, bowls, bowls.
"He likes dot balls and he just doesn't take risks."
Lawson suggested Lyon should get some handy tips on off-spinning from former Test spinner Greg Matthews.
"He needs to have a little chat with someone like Greg Matthews, about how to think people out," Lawson said.
"He could be so much better.
"His stats are pretty good for this stage of his career.
"But, he doesn't really look like getting out the good players."