Orient went close in the opening minutes when Moses Odubajo broke through Tranmere's defence, but he could not control his shot and blasted wide.
Rovers were made to pay minutes later as striker Lisbie finished neatly after great work from Lloyd James, who broke through Tranmere's midfield too easily.
Tranmere's Ash Taylor almost hit back as he headed a Chris Atkinson free kick towards goal, which required goalkeeper Jamie Jones to turn the ball onto the post to keep his side in the lead going into half time.
Orient increased their advantage shortly after the break as Lisbie grabbed his second of the match in the 61st minute.
The visitors clinched their victory in the 68th minute when Cox finished coolly, before Batt added another to help them remain at the top of the League One table.