Lawless was found in breach of the SFA’s zero-tolerance rules by betting on 513 games between December 2012 and March 3 this year, although there was no evidence to suggest he was involved in any of the games.
The 24-year-old was handed a six-match ban in total, but four games are suspended until the end of next season.
A Thistle statement read: “The club and player accept the SFA decision regarding Steven’s breach of the rules around betting on football and won’t be appealing the decision.
“We’re disappointed at Steven’s poor judgement on this issue and have also taken our own internal disciplinary action in line with club policy.
“As a club we have reminded all our staff of the rules to which they must adhere and are also reviewing how we educate our employees on their responsibilities both on and off the pitch.”
Lawless is the fourth player to fall foul of the SFA rules. Earlier this year, the SFA failed in a bid to increase Rangers goalkeeper Steve Simonsen’s punishment for betting on 50 games in a year after two independent panels ruled he should serve an immediate one-match ban.
Simonsen’s team-mate, Ian Black, was previously given an immediate three-match ban for a series of bets over seven years, including three against his own teams.
Then Ayr striker Michael Moffat served a four-game ban after he was found guilty of placing seven bets on six matches involving his own team, as well as a number of other bets.