Thistle stretched their run without victory to eight games when they were held to a goalless draw by Inverness in Maryhill on Boxing Day.
The Jags have only scored three goals in eight home games in the Scottish Premiership and have yet to claim three points at Firhill.
But they dominated against Inverness and created a host of clear-cut chances, a story that has been a consistent theme of their season.
Motherwell are on a three-match winning run, but there is no sign of complacency at Fir Park as they prepare for the short trip into the west end of Glasgow.
Lawson came off the bench during a 1-0 win over Thistle at Fir Park in August and was impressed by the First Division champions.
Lawson told Press Association Sport: "Even when we played them at Fir Park they had a lot of possession during the game, but we managed to get the victory.
"I have spoken to a few boys from other teams who have played against them as well and they have been the same, Thistle have dominated possession and maybe haven't got the luck in front of goal that they maybe deserve.
"So we know it's going to be a very difficult game. They have got lots of very good footballers and they are trying to play the game the right way as well."
Motherwell moved into second place with their 1-0 victory at Aberdeen, which was their first over a fellow top-six side all season.
And Lawson admitted the victory was a special feeling after achieving it against the odds.
The former Ross County and Celtic player said: "The manager had mentioned that we hadn't beaten a top-six side. It's something I hadn't noticed myself but obviously Pittodrie is a tough place to go regardless so it was great to get the win.
"I think a lot of people wrote us off so that was also extra special."