Lisbie's header was enough to claim the three points but Boro will feel frustrated after having a goal chalked off and missing late chances.
The winless hostsstarted the brighter, with winger Luke Freeman causing problems when he crossed into the feet of Daniel Lopez who managed to get a shot away in the 22nd minute.
However, they went behind in the 27th minute when Orient's Moses Odubajo was allowed space out wide to cross a ball into veteran striker Lisbie who headed past goalkeeper Chris Day.
The O's came close to doubling their lead in injury time at the end of the first half when Dean Cox's cross to the back post was just out of the reach of Lloyd James.
Orient picked up where they left off in the first half with David Mooney laying a ball off to Cox who shot just wide soon after the restart.
Lisbie was then put through one-on-one with Day by Mooney in the 64th minute. The striker looked to be brought down by the keeper but was deemed to have dived and given a yellow card.
A corner from Freeman was then met with the head of Peter Hartley which rattled off the crossbar and was cleared off the line by Romain Vincelot in the 73rd minute.
Shortly afterwards, a shot from second-half substitute Greg Tansey was punched away Jamie Jones but only into the path of Darius Charles who rounded the keeper and scored. But it was correctly ruled out for offside.
The last five minutes saw Stevenage building pressure in the Orient half and their final chance fell to Tansey who lashed his shot over in extra-time.