The Jags failed to find a way past Cowdenbeath in 90 minutes on Tuesday night before extra-time strikes from Lawless and Christie Elliott and an Aaron Muirhead penalty gave them a 3-1 win and a League Cup third round berth.
Turning their possession into goals has proven tricky for Alan Archibald's side at times this season, with a host of chances passed up in their Premiership encounters with Dundee United and Hearts and a second-half onslaught yielding no rewards against Motherwell last weekend.
Boss Archibald handed a start to summer signing John Baird for the Blue Brazil clash in midweek and deployed Lawless, Elliott and Kris Doolan from the bench as the Jags finally saw off Colin Cameron's side.
And Lawless is confident the floodgates will soon open for the Firhill forward line.
He said: "I thought the boys played well. We need to start taking chances I think but, other than that, it was an OK performance and getting through was the most important thing.
"It would be worrying if we weren't creating chances.
"Dools and Bairdy are good strikers and they are going to score goals. It is not just them. I missed a couple of chances when I came on as well.
"Once they get a couple in them, I am sure they will start banging them in and it will be the same around the team. I could have had a few on a different night."
Thistle were far from their free-flowing best on Tuesday night, but still deserved to clinch a third-round berth as they dug deep to emerge worthy winners.
Lawless was instrumental for the Jags after coming off the bench and the striker was pleased with his night's work.
He said: "It went pretty well when I came on, but I thought I could have had a couple more assists, I got Dools in for one or two.
"We are just glad to get through. It was good to get the goal and the assists as well. That is confidence for the boys."
Thistle may have been pushed all the way by their former First Division rivals, but they avoided following Premiership peers Kilmarnock and St Mirren in crashing out of the cup on an anxious evening for a host of top-flight teams.
And Lawless hopes this can be the Jags' year to embark on a run into the latter stages of a cup competition.
He said: "We saw when we went in that some Premier League teams went out. You can't take it away from the other teams, they must have put in good performances against them.
"It is a hard game for most teams, as we found out. It is a tough game.
"We will just look forward to the draw now and see who we get in the next round.
"If we didn't think we could win the competition there would be no point playing in it.
"We just need to take it a round at a time. We are happy to get through this round.
"Hopefully we can put a wee run together because we have not really done that well in the cups over the years.
"Last year we were doing well and we were hoping to get an SPL team to see where we were. That didn't happen and we got put out by Hamilton and Dunfermline.
"We know teams are going to come here and up their game against us. We need to take it the other way and put in professional performances to get the result."