Brig face Matlock Town at the Sir Tom Finney Stadium tomorrow and then travel to Marine on Monday.
The 2-0 victory over Hyde ended a nine-game losing run for Brig and gave their hopes of avoiding relegation a shot in the arm.
Beating Matlock would see them climb out of the bottom three and above Mickleover, who are not playing.
Lawlor, in joint charge with Joey Collins, said: “We did really well at Hyde and now we have to do that again when we play Matlock.
“It’s not enough doing it once, we need to back it up in the remaining games.
“Tomorrow is our game in hand over Mickleover, who aren’t playing.
“We would like to make the best of that and hopefully after the Easter games we can be in a better position than we are now.”
Ahead of the Hyde game, Lawlor arranged a friendly with AFC Blackpool.
And he felt the 3-0 win in that bounce game gave them something to build on. Said Lawlor: “We played behind closed doors against AFC Blackpool and it was an opportunity to give some of the lads a game and break up the rhythm of training.
“It might only have been a friendly but it gave all the lads a lift to win it and we took that into the Hyde game.
“With a friendly win and a victory in the league, we have just started to build up a bit of momentum which we need at this vital stage.”
Matlock are in 13th place ahead of their trip to Brig but Lawlor doubts they will have their flip-flops on.
“You might hope that they are in holiday mode but I very much doubt it,” said Lawlor.
“In Dave Frecklington they have a very competitive and very good manager, he will have them up for the game.
“We had a right battle with them down at their place in November, there was a time in the second half when we were getting a battering.
“They have a lot of quality, their four attacking players are a handful.
“Matlock is our focus to start with, once we’ve played them we will move on to look at Marine on Monday.
“Marine are one of the sides down there with us. If we can get a win against Matlock, it would take a bit of the pressure off Monday.
“We are looking forward to the games which are close together.”
Brig are without Callum Spooner who is suspended following a red card against Scarborough Athletic earlier in the month.
Lawlor revealed that Jake Phillips had left the club due to injury.
He said: “Jake suffered a recurrence of an injury which he’s had a few times before so he’s just stepped away from football for the moment. We wish him all the very best.”