The visitors' goals were scored by Carl Baker and Franck Moussa although Baker was sent off after 55 minutes for a late challenge on Romain Vincelot.
The Sky Blues also missed a penalty when Jamie Jones flung himself to his left to save Leon Clarke's effort.
Coventry's misery was compounded when Lisbie headed home the winner with one minute of normal time remaining.
Baker had put his side ahead after 22 minutes when he turned full-back Gary Sawyer inside-out and then drilled a left-foot effort into the far corner of the net.
That acted as a wake-up call for the home side and within four minutes they were back on level terms. David Mooney had a shot blocked by goalkeeper Joe Murphy but Lisbie raced on to the rebound to fire his shot home from 15 yards.
Orient took the lead after 37 minutes after a free-kick had been blocked and winger Cox rifled in a shot through a crowded goalmouth from just outside the area.
Despite being down to 10-men, the visitors equalised when Moussa, who had previously hit an upright, sent a superbly-placed shot into the net in the 59th minute.
City had the chance to take the lead when Scott Cuthbert felled Clarke after 76 minutes but the spot-kick was saved and with time running out, Moses Odubajo sent over a pin-point cross for Lisbie to meet and head over Murphy for the last-gasp winner.