The point was no more then the Londoners deserved after dominating the game for long periods.
But it was Lincoln, chasing an automatic promotion spot, who looked like taking all three points after Simon Yeo struck after just three minutes.
The City striker, in a rich vein of form, grabbed his 17th league goal of the season when he raced on to a through ball and delicately lobbed Orient goalkeeper Lee Harrison.
The early goal warmed up Orient's lowest league gate of the season after the kick-off had been delayed for 30 minutes because of a problem with the floodlights.
Ironically the home side looked to have started well as Daryl McMahon went close with a 20-yard drive that flashed over Alan Marriott's bar after two minutes.
But 60 seconds later the visitors were ahead when Yeo scored for the seventh consecutive game.
After that Orient made most of the running but for all their possession they failed to create many clear-cut chances.
It was former Orient striker Gary Taylor-Fletcher who almost stretched Lincoln's advantage when he headed just wide on 28 minutes.
Orient returned to the attack and on a stroke at half time Marriott saved superbly from McMahon following Justin Miller's excellent run.
The second half followed a similar pattern and Marriott was soon in action as he parried a shot from Tom Youngs and then Lee Steele saw his follow-up effort blocked.
Lincoln were dangerous on the break and Matthew Lockwood had to scramble another effort from Yeo off the line, but Orient's perseverance was finally rewarded seven minutes from time when Miller's long throw was met by Mackie whose looping header drifted into the far corner for his first goal of the season.