Bristol City are on course for three vital points that will lift them out of the relegation zone.
The visitors took the lead with just three minutes on the clock, as Jay Emmanuel-Thomas's cross-field pass was met by Sam Baldock to fire the Robins ahead.
It was two soon after courtesy of Tyrone Barnett, with the striker heading home Marlon Pack's corner to put City on course for the points needed to lift them to safety.
Baldock had the ball in the back of the net again moments later, though the referee had already blown his whistle after Aden Flint challenged Shwan Jalal in the Orient goalmouth.
Orient players appealed for a penalty after Chris Dagnall fell down in the box, but Steve Cotterill's side played on and nearly scored at the other end after Baldock and Greg Cunningham combined well.
The O's managed to pull a goal back just before the half-time interval, with Lisbie the quickest to react following a shot that Simon Moore could only parry.
