Thomas Gravesen scored the goal midway through the first half which ensured Celtic gained all three points, but it was the incredible scenes at the end which will remain in the mind.
After being denied a penalty in last week's match against Rangers, Lennon went down under Kenny Milne's challenge and referee Ian Brines awarded the penalty.
Falkirk protested and in the ensuing melee Lennon appeared to raise his hands to both Milne and Anthony Stokes. The Celtic skipper was ordered off with Milne and Stokes both booked.
It seemed almost incidental that substitute Kenny Miller struck his spot-kick against the post after Lennon had stormed off the park, throwing his captain's armband to the ground and also having further words with the linesman.
After chances at both ends, Celtic took the lead when Gravesen won a tussle at the edge of the box before lashing a tremendous right-foot shot into the top corner.
After the interval Falkirk continued to play attractive one-touch football.
Jiri Jarosik squandered a gilt-edged chance and Paul Telfer tested Scott Higgins with a powerful volley before Falkirk came to close to equalising.
Artur Boruc made a great save from Stokes then did well to block the rebound from Stephen O'Donnell.
However, the Celtic keeper could do nothing when Alan Gow skillfully sped past Lennon before chipping his effort over Boruc, only to see the ball come back off the bar.
Falkirk continued to press before the game ended in mayhem with that Celtic penalty miss seven minutes into injury time.