The talented midfielder scored either side of half-time to ease the visitors into a two-goal advantage.
Lady Imps striker Carla Cantrell pulled one back for the hosts on 54 minutes and despite a spirited fight-back, Blues clung on for a vital win.
Speaking after the game, Blues boss David Parker said: “This season will go right down to the wire. There is a long way to go yet and this win has put us in the mix.
“This is a fantastic result because Lincoln have some very good players. But we deserved it and if anything we should have seen the game out more comfortably than we did in the end.
“We should have kept a clean sheet and even added a few more at the other end. But we are determined to put the wrongs of the opening half of the season right and this is a very good start.”
The visitors were always in command of the match.
Jo Potter saw her curling 35-yard free kick superbly tipped over by Lincoln shot-stopper Karen Bardsley after just three minutes.
Lincoln responded with a free-kick of their own moments later when skipper Casey Stoney rattled the crossbar from the edge of the box.
Bardsley was forced into action again on 12 minutes when, following a flowing move, Kirsty Linnett cut inside and drew the home goalkeeper into a fine save.
The deadlock was broken in style on 32 minutes. Lawley picked up the ball just inside the Lincoln half and, after being allowed to run and run, unleashed a sublime curling effort into the top-right corner from 20 yards.
Lawley showed perfect composure soon after the break to double the lead. A long punt forward on 47 minutes was expertly controlled by the winger in acres of space, before she calmly slotted the ball past a helpless Bardsley.
To their credit, the Lady Imps continued to fight hard and halved the deficit seven minutes later. A perfectly-weighted ball by Lillie Fenlon-Billson was poked home by onrushing strike partner Carla Cantrell – much to the delight of the home faithful.
The hosts huffed and puffed but failed to create any clear-cut chances as Birmingham hung on to move five points clear of their opponents in the table.
Parker added: “It was a huge win. Mel’s first goal in particular was absolutely fantastic. That is what she has in her locker, like a lot of our players, and she is class.
“We will prepare for Doncaster now next week and despite their low position in the table, we know what challenge they will pose.
“We will go all out to win though as we look to continue climbing the table.”
Lincoln: Bardsley; Fay, Stoney, Bradley, Cantrell (Whelan 68); Allen, Clarke, Walton; Martha Harris, Fenlon-Billson (Lee 68), Roberts (Sweetman-Kirk 45).
Subs not used: Draycott, Horwood, Sargeant.
Blues: Spencer; Weston, Harrop, Christiansen, Linnett; Potter, Moore, Lawley; George (Bassett 71), Westwood (Carney 63); Wilkinson (Williams 63).
Subs not used: Simpkins, Torkildsen, Earps, Haines.
Referee: D Carratt