Teenage striker Robert Snodgrass gave Livingston an invaluable point with an 88th-minute wonder strike.
Falkirk looked to have the points wrapped up through an early own goal from Harald Pinxten, but Livi battled back well in the second half and gave the 2000 odd Livi supporters something to celebrate.
Snodgrass picked up the ball wide on the left, beat a couple of Falkirk players and then curled a superb shot past Matt Glennon.
Falkirk started the brightest and Darryl Duffy had an opportunity after only three minutes when Russell Latapy set him up, but his shot thumped against Roddy McKenzie's right-hand post. It was a let off for Livingston, and surprisingly, Lambert decided not to man-mark Latapy, a move that frustrated the Livi support.
Latapy then attempted to beat McKenzie with a 25-yard free-kick which dipped below the crossbar, but McKenzie managed to flip the ball over the top.
Roddy yet again was badly at fault after 15 minutes when Falkirk were gifted a goal. He missed Craig McPherson's corner and the ball struck the head of defender Pinxten and went into the empty net. Roddy is lacking confidence at the moment, and his cock-up will lower that even more.
Latapy was proving a thorn in the flesh with his trickery up front and he set up another chance for Duffy, but the angle was tight and McKenzie plucked his chip out of the air. Lambert was showing his in-experience as a manager with letting Latapy run free in the midfield, and Livi were lucky to go in at half time only one down.
Snodgrass tested Glennon again early in the second half with a shot from distance which the goalkeeper batted down and gathered at the second attempt.
Duffy had the ball in the net for Falkirk after 49 minutes but was ruled offside from Latapy's first-time pass.
Livingston brought on James McPake for Neil Barrett 10 minutes later and Jimmy Scott dropped back to midfield, and they carried more threat after that.
Pinxten was not far away with a terrific shot from the edge of the area which beat Glennon but skipped just wide of the post.
It was a clear warning to Falkirk who continued to pass the ball well, but too often wasted the final ball when they closed in on McKenzie's goal.
Latapy set up a great opportunity for Stephen Thomson after 72 minutes, but McKenzie leapt to his left to get a hand to the ball and push it to safety.
A big well done to all the Livi supporters that travelled to the match. If you would like to go to Livi matches away from home, itβs easier than you think. There are three supporters club busses that travel to every game. The Livi Lions Supporters Club contact number is β 07802 765900.
The Trinidad & Tobago international was then denied a goal for himself when his 12-yard shot struck the head of Greg Strong just when it looked a certain goal.
The Official Supporters Club contact number is - 01506 439558
The Gus bus travel club contact number is β 01501 751281