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.