Jackie McNamara's side have got off to a 100% start in the league, winning all five games.
They currently sit three points clear of nearest title rivals Dunfermline and there is a particular kind of pressure that comes with being the pack leaders.
Lawless, though, believes that the Firhill side are able to hold their mettle.
"I think the manager has always said that he would rather have this type of pressure than the pressure of struggling in the league, so I don't think it is something that we have to worry about," said the former Motherwell man.
"We aren't getting too bogged down in what might be. We're just concentrating on each game and trying to make sure we come out of it with a positive result.
"We've Cowdenbeath this weekend and that will be another hard one. In this league, there is so little between the teams, so it's important that we just try and keep the run going as long as we can."
Lawless netted a brace against Livingston at the weekend to maintain the impressive start he has had to his Thistle career.
McNamara spoke in glowing terms about the player after the weekend game, but the 21-year-old is just delighted to be in the position where he is playing regular football and making a fantastic contribution.
"I'm enjoying it here," he smiled. "I've had the chance to come in and show what I can do and I'm trying to make the most of it.
"The manager has built a team that has a lot of young boys in it like myself who have come in and are just trying to show that they want to play.
"But there is a lot of ability in the side. Going forward I think we are always a threat and the good thing is that we are always creating chances in games. Long may that continue."
Having finished sixth last term in the First Division, Thistle have been something of a surprise package this term as they have set down an early marker.
Lawless, however, has not been surprised at the way Thistle have gone about their business since the league campaign got underway.
"I think we might have surprised a few people, but I think there was a quiet confidence about us at the start of the season," he said.
"You don't know what might happen as the season progresses and you have to hope the squad will cope if there are injuries and suspensions, but we've started well.
"All we can do is keep working hard and hope that we keep that going."