They didn't even need top scorer John Hartson, who grabbed a hat-trick on his last visit to West Lothian back in April, but this time contributed just nine minutes as a late substitute after manager Gordon Strachan preferred Maciej Zurawski upfront.
And then again recent history - Celtic scored eight times in two visits last season - suggested that Strachan could have won the match with any 11 players wearing green and white hoops.
Sure enough Celtic cruised to their fifth SPL win on the trot to close to within two points of leaders Hearts who they welcome to Glasgow on October 15.
A delighted Strachan said: "In total football and imagination that was as well as we have played this season. We started well and scored our goals at the right times which was handy.
"I don't think there were any weaknesses today at all which was great. Livingston tried to make it cup-tie football and we had to avoid that which we did.
"I thought our front six were fantastic today and I felt the movement and understanding especially for the second goal was outstanding."
At the opposite end of the league table, winless and hapless Livingston remain three points adrift of the pack, leaving Lambert with a job so tough that lifting the European Cup with Borussia Dortmund must seem like child's play.
Lambert said: "There is no point coming in on Monday and being down about this. We just have to go again.
"Nobody expected us to take anything from Celtic today, but if you had spoken to me after 40 minutes then I thought we were doing fine. Unfortunately the game lasts 90 minutes.
"Even at 1-0 you are always in it, but the second goal made things much more difficult and the third one finished us. Make no mistake, Celtic are a very good side but up until the first goal there wasn't much in it.
"Our players gave every bit of effort that they could and I know myself how difficult it is to lose 5-0, but they kept going to the end."
The name Dalglish will always be closely associated with Celtic, but Livingston striker Paul almost cancelled out father Kenny's legendary status when he shot narrowly wide after only four minutes.
Japanese midfielder Shunsuke Nakamura produced a more threatening effort for the visitors just two minutes later and home goalkeeper Roddy McKenzie took no chances with the swerving 20-yarder as he punched it away for a corner.
With Nakamura and skipper Stilian Petrov pulling the strings, Celtic were controlling the possession but Livingston cleverly used any scraps that fell their way and Derek Adams and Graham Barrett nearly set up Dalglish after central defender Bobo Balde had been caught of position.
Barrett then surged powerfully into the Celtic penalty area, but Chris Sutton drifted back from midfield to muscle him off the ball.
Enough was enough for the Hoops who punished Livingston's cheek by dominating the rest of the match. Young striker Craig Beattie twice tested McKenzie before full-back Paul Telfer warmed his fingers with a fierce angled drive.
Slowly but surely Celtic were edging closer to the all-important opening goal and in the 27th minute a curling left-foot free-kick from Nakamura missed the target by a fraction. Moments later a deliberate side-footed shot by Petrov flashed a matter of inches the wrong side of the post.
Finally, nineminutes before half-time, an inswinging corner kick from Shaun Maloney found Sutton whose head-flick was forced home from close range by defender Steven McManus.
Celtic's confidence was high and they underlined their superiority in first-half injury time when Maloney rounded off a superb one-touch passing move with a low finish into the far corner of the net.
Rather like circus performers, Celtic's players were now desperate to show off their skills and six minutes into the second period left-back Mo Camara delivered a cross straight on to the forehead of Zurawski, who gobbled up his fifth goal of the season from eight yards.
The fourth goal was perhaps the best of the lot as Sutton latched on to a blocked free-kick from Maloney and hammered a sweet half-volley high into the roof of the net.
If that was the sublime then the ridiculous was soon provided by the home defence, which somehow allowed another Camara cross to find its way to Beattie who tapped the ball in almost apologetically.
Celtic could easily have made it six barely two minutes from the final whistle, but McKenzie deserved great credit for his spectacular one-handed save as he pushed a netbound effort from Petrov around the post.
Man of the Match: Stilian Petrov - Gave a captain's performance in the absence of Neil Lennon. Driving the Bhoys forward at every turn as they roared to an easy victory.