The 25-year-old Victorian is set to play his first Test in Australia on Boxing Day, beating out Matt Kuhnemann and Corey Rocchiccioli for a spot in the 15-man squad.
As expected, captain Pat Cummins will sit out the match as he protects his body following a serious back injury this year.
Cummins conceded after the win in Adelaide he would be unlikely to feature at the MCG.
If Steve Smith is fit after a vertigo episode forced him to miss the third Test, the star batter will again captain Australia in Cummins' absence.
Western Australian quick Jhye Richardson is in contention to play his first Test in more than four years after being recalled to the squad.
Richardson has endured a torturous run with injury, but has made a flawless return to cricket in recent weeks.
Australia will need to replace Cummins so Richardson will be battling it out with Brendan Doggett and Michael Neser for a spot in the XI.
A decision must be made on who makes way for Smith, with Usman Khawaja and Josh Inglis likely vying for one spot.
Lyon tweaked his hamstring while diving to save a boundary on the final day of the third Test in Adelaide, where Australia retained the urn with an 82-run win over England.
The 38-year-old has enjoyed an injury-free run through most of his Test career, with the other setback of note being a torn calf in the 2023 Ashes.
Murphy replaced fellow offspinner Lyon in Australia's XI after that 2023 setback at Lord's.
Lyon's hamstring injury is expected to sideline him for months, but Australia's next Test after the Ashes finishes isn't until September or October in South Africa.
AUSTRALIA: Steve 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.
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