Brig were three down inside 35 minutes at Gainsborough on Tuesday, and eventually lost 4-1 despite Kieran Charnock's second half header.
That result extends their winless streak on the road to seven in the league this season.
And captain Lawlor said of the performance: "The first half on Tuesday absolutely killed us.
"Mistakes need to stop happening and we need to bring a stronger mentality to the group.
"There were a huge amount of positives that came out of Saturday (against FC United) but we need to repeat that type of performance.
"We need to play to the same structure that we are used to and one we've had success in the past with, and we're going to graft and put in a much better performance on Saturday against Witton."
Brig's home record, however, has seen them win two out of their three games so far this campaign, and Lawlor wants that form to continue.
The first team coach said: "It will be nice to get back to our home pitch where we can look to get three points.
"It's our home patch - the groundsman has done an unbelievable job with the pitch as we like to play football and it needs to be a win for us on Saturday, nothing else will do."
Lawlor was keen to stress, however, that Brig are looking to pick up three points in every game they play, regardless of where it is played.
He added: "At home we've got to win, we know that, but away from home we need to start picking up points.
"I don't feel (the amount of away games) has been an influence.
"It's a game of football at the end of the day, it doesn't matter whether we're in Gainsborough, in Manchester or at home at Bamber Bridge, we've got to approach it the same way and we can't let anything become a hurdle.
"Whether it's against PNE at home in pre season or Witton Albion on Saturday, we aim for three points. We've got to win at home - that's the aim."
Lawlor also spoke about the news that Brig have been awarded the status of an FA Charter Standard Club by the Lancashire FA yesterday.
He said of the achievement: "We've had a succession of coaches in terms of Crowey as manager, then Reno and the likes of Micky, Joey and myself coming in.
"I think it's a reward for the club and all the work they do behind the scenes as well.
"There's so many volunteers that the club won't exist without, it wouldn't exist without the chairman not financially backing it but running the club on a voluntary basis.
"The amount of work that goes on behind the scenes is unbelievable and it's a big pat on the back to everyone within the club.
"We want to try and get as high as we can as quickly as we can which is the aim, and it's a massive well done to everyone."