Khawaja, 38, had back spasms and failed to open in the first Test victory against England in Perth then was ruled out injured for the second in Brisbane.
He has since recovered, but selectors opted to stick with Travis Head and Jake Weatherald at the top of the order, leaving the veteran's international future in doubt.
As expected, Cummins returns after missing the first two Tests with a back injury, leading the attack alongside the outstanding Mitchell Starc and Scott Boland.
Veteran spin king Lyon is also back after being axed in preference for an all-pace attack at the Gabba.
Brendan Doggett and Michael Neser make way.
Australia third Test XI:
Jake Weatherald, Travis Head, Marnus Labuschagne, Steve Smith, Cameron Green, Josh Inglis, Alex Carey (wk), Pat Cummins (capt), Mitchell Starc, Nathan Lyon, Scott Boland