The hosts raced out of the traps and could have gone ahead through Lisbie - who passed a late fitness test to start - but Dons defender Dean Lewington produced a last-gasp challenge to deny the 34-year-old from pulling the trigger.
With their undefeated record under some threat, Orient responded well to the setback and could have been awarded a penalty, as David Mooney went down under pressure from Tom Flanagan but the referee shrugged off appeals by the home players.
However, the hosts were soon level. Mooney wriggled down the right and crossed for Odubajo, who dispatched a curling effort past McLoughlin to preserve Orient's hopes of extending their unbeaten run.
Slade's charges failed to begin the second half with the same momentum prior to the interval and could have fell behind once more as Bamford again menaced, but the Irishman's volley cannoned off the chest of captain Nathan Clark.
The comeback was complete on 68 minutes, as Mooney and Lisbie exchanged a neat one-two, before the latter poked past McLoughlin inside the area.
Lisbie was given a standing ovation when he departed the field for Shaun Batt minutes later, and the 26-year-old was involved immediately, forcing McLoughlin into a smart save.
Orient's resilience to claw their way back into proceedings was nearly rendered futile when Izale McLeod saw his effort cannon off the frame of the goal in the dying minutes, but the East Londoners held on to preserve their undefeated run.