Lyon was ruled out for the rest of the series by a hamstring injury sustained as Australia beat England by 82 runs in the third test in Adelaide on Sunday to clinch the series and retain the Ashes.
Steve Smith was also named in the squad despite missing the third test after suffering a bout of vertigo and will captain the side in the absence of Cummins, as he did for the first two tests of the series.
Cummins, who took six for 117 in Adelaide, is still on the road to recovery after suffering a back injury and is likely to be replaced in the bowling attack by Brendan Doggett or Michael Neser, who have already played in the series.
"(Pat) won't play any part in the rest of the series," coach Andrew McDonald told reporters at the Melbourne Cricket Ground on Tuesday.
"We were taking on some risk (with him) and 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."
Jhye Richardson, who trained with the team in Adelaide, has also been called into the squad as a further pace option after fine domestic form on his return from shoulder surgery.
Murphy, 25, has played seven tests since his debut in India in 2023 and has long been considered the heir apparent to Lyon.
All-rounder Beau Webster, who has yet to see any action in the series, also offers part-time off-spin and is another option to replace Lyon at the MCG from Friday.
"Todd's been an important part of a key overseas series. He played in the last Ashes back in 2023 and we feel as though Todd's back to his best," McDonald said.
"We've got some decisions to make. Do we play a spinner? Don't we play spinner? We'll work through that."
McDonald said 38-year-old Lyon, who had surgery on his injury earlier on Tuesday, was "devastated" but had already turned his thoughts to being back in the side for the tour of India in early 2027.
"It's gonna be a hard period for him to get back to where he was but he still wants to do it, and that's the main thing," the coach said.
Top-order batsman Usman Khawaja retains his place in the squad despite being dropped from the team for the Adelaide test, only to be recalled at the last minute when Smith was ruled out.
McDonald also wouldn't lock Cameron Green into the XI, leaving open the option of a recall for fellow all-rounder Beau Webster.
"He hasn’t got the runs that he would like,” McDonald explained.
“I think he has bowled some important spells for us. His catching in the gully and shot-stopping ability is there. The returns haven’t been there, but we’ve also seen what capabilities and the upside that he has, and he’s an important part of what we’re setting out to achieve in the short term and the long term.
"He’s a very good cricketer, and I’m sure that his next opportunity, he’ll be able to show that whenever that may be.”
Australia 4th Test squad:
Steve Smith (captain), Scott Boland, Alex Carey (wk), Brendan Doggett, Cameron Green, Travis Head, Josh Inglis, Usman Khawaja, Marnus Labuschagne, Todd Murphy, Michael Neser, Jhye Richardson, Mitchell Starc, Jake Weatherald, Beau Webster