Jackie McNamara's men got the breakthrough in the 36th minute when the 21-year-old former Albion Rovers striker unleashed a stunning 25-yard shot which found the net via the crossbar.
The league leaders doubled their advantage three minutes into the second half when Paul Paton's measured pass found Lawless and he sprung Livingston's offside trap to net his second of the game.
Partick had to survive a nervy final half-hour after Jordan Morton powered home Iain Russell's flick-on in the 58th minute but Livingston could not find a leveller.
Still three points behind Partick are Dunfermline Athletic who won 2-0 away to bottom club Dumbarton. The first half was a tightly-fought affair but Andy Kirk fired the visitors in front from a Josh Falkingham cross after 41 minutes.
Falkingham was also the creator of Dunfermline's second goal seven minutes into the second half when he picked out former Burnley and Manchester City defender Stephen Jordan, who slotted home in style.
Raith Rovers climbed to third place with an impressive 2-0 victory over Airdrie United at Stark's Park. Brian Graham opened the scoring against the run of play in the 37th minute as the visitors' normally prolific Ryan Donnelly had an off day. The free-scoring Graham nearly doubled his tally but was denied by the woodwork.
However, Raith did add a decisive second goal in the 83rd minute when Allan Walker crossed for Greig Spence to head home from close range.
Cowdenbeath's good run came to an end as they fell to a 4-3 defeat against Morton at Central Park. Peter Weatherson headed the visitors into a 12th minute lead before adding second from a David Graham cross.
John Armstrong halved the arrears five minutes before half-time, heading home from close range, only for Archie Campbell to restore Morton's two-goal advantage a minute after the restart.
David O'Brien's 54th-minute strike gave Morton a three-goal cushion before a late rally almost salvaged a point for Cowdenbeath, with Mark Ramsay and Jamie Stevenson netting in the last eight minutes.
Hamilton Academical and Falkirk shared the spoils in a 1-1 draw at New Douglas Park. James Keatings and Louis Longridge both went close for the hosts before Lyle Taylor netted a fifth-minute opener for Steven Pressley's men.
Hamilton were back on level terms three minutes before the interval when Longridge set up Jon Routledge for a slick equaliser.
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