It looked like Vale would become the first team to take any points off Orient in Sky Bet League One this season as Louis Dodds and Jennison Myrie-Willams scored either side of two goals by David Mooney, but Lisbie made it six wins out of six for the O's with the decisive strike after 88 minutes.
Orient fell behind for the first time in a league match this season when a cross from Tom Pope after 21 minutes eluded goalkeeper Jamie Jones and Dodds headed the ball home from 12 yards out.
Mooney crashed home an unstoppable equaliser from a similar distance just three minutes later, although Vale protested angrily for an offside decision.
The home side grew in confidence and on the stroke of half-time Mooney gave them the lead. Midfielder Romain Vincelot dispossessed Chris Robertson and teed-up the striker to slide the ball under keeper Chris Neal for his for his seventh league goal of the campaign.
Although the O's enjoyed the better of the opening exchanges after the break with Lisbie twice going close to extending their lead, the visitors got themselves back on level terms after 53 minutes. Jones was only able to palm away a cross from Doug Loft and Myrie-Williams struck a left-foot volley into the back of the net.
However, with two minutes of normal time left, Lisbie held off the challenge from two defenders before lashing the ball home from 10 yards out to extend the league leaders' run to six wins from as many matches.