Cummins will miss the remaining two Tests of the series as the captain continues to manage his back injury while spinner Lyon is set to got for surgery on a torn hamstring.
The home side have added slow-bowler Todd Murphy and paceman Jhye Richardson to their 15-man squad.
Steve Smith, who missed the third Test in Adelaide due to illness, will return as captain in the absence of Cummins.
Australia head coach Andrew McDonald said of Cummins: "We were taking on some risk and people that reported on that would understand the risk associated with that rebuild.
"We've now won the series and that was the goal. So, to position him for further risk and jeopardise him long-term is not something that we want to do and Pat's really comfortable with that."
While Murphuy seems a shoe-in to replace Lyon in the XI, McDonald did not ruled out playing an all-pace attack in Melbourne.
Australia Test squad: Steven Smith (capt), Scott Boland, Alex Carey, Brendan Doggett, Cameron Green, Travis Head, Josh Inglis, Usman Khawaja, Marnus Labuschagne, Todd Murphy, Michael Neser, Jhye Richardson, Mitchell Starc, Jake Weatherald, Beau Webster.
Australia secured the 2025 Ashes with victory in the third Test on Sunday, bringing a broad smile to Pat Cummins’ face, but opposing captain Ben Stokes was wallowing in the mire.
England put up a fight, but ultimately Australia grabbed the four wickets they needed for an 82-run victory in the third Test and secure the Ashes 3-0 on Sunday.
England are staring down the barrel of an Ashes series defeat after Australia's Nathan Lyon broke their resistance late on day four of the third Test in Adelaide.
Nathan Lyon became Australia's second-highest Test wicket-taker after Shane Warne in day 2 of the third Ashes test in Adelaide on Thursday.
