The 24-year-old was handed a six-match suspension by an SFA disciplinary tribunal, but four of those are suspended until the end of next season.
He will serve those should he be found to break the rules again before then.
Lawless had been accused of betting on 513 matches between December 2012 and March 2015.
SFA disciplinary rule 33 prohibits players, coaches, club officials and referees in Scotland from betting on football anywhere in the world.
There was no evidence to suggest that Lawless was involved in any of the games, but Thistle expressed disappointment at the player's actions.
"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," the Glasgow club said in a statement.
"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 United 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.
Partick Thistle midfielder Steven Lawless will miss two matches after being found guilty of breaching Scottish FA rules on gambling.