Earlier, Max Dearnley had produced more heroics as he saved a third penalty of the season, but with 10 minutes remaining a deflected strike from Lambert proved to be the difference between the sides.
The hosts did come flying out of the traps in the early stages, and were perhaps unfortunate to not have found the opener in the first quarter of the game.
Adriano Moke and Kaine Felix both had early chances only to be denied by Dearnley, Moke, in particular, producing an excellent save low down from the Farsley shot-stopper.
It would be Felix who came closest to finding the opener midway through the first half; An acrobatic volley on the turn from a Kallum Griffiths centre cannoned onto the crossbar with Dearnley beaten.
Farsley would grow into the game and ease the pressure on their goal, and began to fashion openings of their own.
Shortly before the interval, Frank Mulhern found Jimmy Spencer in the box who carved out space for a shooting opportunity, only to be denied as Darlington threw bodies in the way.
The start of the second period would be a different story, however, with the Celts pushing forward and striving for the opener.
Neat link-up play down the right between Lewis Turner and Spencer saw the former find Mulhern in the box, who shot straight at Tommy Taylor, before Spencer would see a strike deflected just wide.
Spencer then came inches away from handing his side the advantage, glancing a near-post header from Bobby Johnson’s delivery agonisingly wide of the far upright.
Within 60 seconds of that missed opportunity, the referee was pointing to the spot at the other end, as Tom Allan was adjudged to have committed an infringement in the box.
But Dearnley was up to the task, guessing correctly to make a fine save from Lambert.
Farsley were then aggrieved not to be awarded a penalty of their own, as Andy Butler appeared to be clattered into from behind in the box.
And the sucker-blow would arrive as Lambert’s strike took a wicked deflection off Butler to deceive Dearnley, and hand the hosts all three points.
Darlington: Taylor, Sukar, Lawlor, Hedley, Moke © (Liddle 74), Hazel (Rivers 79), Lambert, Back, Purver, Griffiths, Felix (Mondal 63). Unused subs: Rose, Emery.
Farsley Celtic: Dearnley, Turner, Scales, Johnson (Syers 83), Butler, Clayton, Allan, Atkinson ©, Spencer, Mulhern (Malumo 76), Parkin (Gratton 76). Unused subs: Morgan (GK), Dube.