The table-toppers turned in a stellar performance at Brisbane Road as they fully stretched bottom-of-the-league County, who spluttered against the high tempo of the home side.
Lisbie started the goal rush in the 28th minute when he ran on to a superbly delivered Lloyd James free-kick and headed the ball down and past Bartosz Bialkowski.
His second on the stroke of half time owed much to good refereeing by Rob Lewis, who played the advantage allowing David Mooney to race down the left before threading the ball through to Cox.
The diminutive midfielder's shot was blocked, but the ball rebounded to Lisbie who drilled the home from 15 yards to give the O's a comfortable lead at the break.
Cox himself added to the party atmosphere 11 minutes into the second period when he curled his low shot into the net off the far post.
In a rare Magpies raid, unmarked substitute Danny Haynes pulled a goal back with a header, before Shaun Batt restored the three-goal advantage - squeezing a shot past Bialkowski after scampering away from two defenders.
County's miserable night continued when Jayden Stockley netted in the 84th minute to record his first goal since joining Orient on loan from Bournemouth.