Forrester grabbed his fifth goal in seven games with a cool lob from 20 yards over the head of O's keeper Glyn Garner. The 36th minute goal stunned Orient who had controlled the game up to that point.
The O's were desperate for victory to keep them with a chance of promotion and got off to an excellent start. Matt Lockwood swung in a corner which was headed home at the far post by John Mackie with just 75 seconds on the clock.
Orient should have gone further in front in the ninth minute when Gary Alexander set up Donny Barnard but the midfielder's shot flew narrowly wide. Then Craig Easton was left unmarked on the edge of the six-yard box but failed to find the target with his header.
Lincoln's first attack came in the 29th minute when Jeff Hughes sent in a deep cross which was won by Marvin Robinson but the striker's header was just too high.
Two minutes later Orient could have gone further in front. Alexander got across the Lincoln defence and found the target with his header but Francis Green cleared off the line.
Orient were continually penalised by referee Trevor Parkes and conceded one free kick too many in the 36th minute.
Alexander fouled Gareth McAuley and from the free-kick Lincoln worked the ball to Green. The big striker held off his marker and laid off a pass to Forrester who found the net.
Lincoln improved in the second half but could not find a way through for the winner. Green burst through on the hour only to be wrestled to the ground by Gaby Zakauni on the edge of the box.
The free-kick from Scott Kerr came back off the defensive wall and Nat Brown followed up with a thunderous shot which flew wide.
Seventeen minutes from the end Garner fed a clearance straight to Forrester but managed to get back in his goal to save the striker's 40-yard shot.
Wayne Corden and substitute Lee Steele had late chances for Orient but in the end both teams had to settled for a draw.