One consolation from this Ashes defeat has been the success of less experienced players Dawid Malan and Craig Overton, while Stoneman and Vince have shown glimpses of belonging at this level.
But England, who are set to hand 20-year-old Mason Crane his Test debut at the SCG after Tom Curran's introduction in Melbourne, want to consider the best batsmen from the Lions set-up when they select their squad for New Zealand.
"There's been some chat about how we can start to get younger players in the side," said England coach Trevor Bayliss. 'Livingstone, Clarke and Lawrence have all been mentioned."
Lancashire's Livingstone, 24, made two full Twenty20 international appearances last summer but struggled against South Africa. He is a rare, explosive talent, though, and highly rated by England, who believe the hard-hitting Cumbrian — just like Ben Stokes — could be a better bet in the red-ball game.
Lawrence of Essex has caught the eye of Bayliss and, at 20, has been considered one of the best batting prospects in the domestic game since he scored 161 against Surrey aged 17. Clarke impressed as a late call-up in place of Ben Duckett for the warm-up match in Perth ahead of the third Test.
He hit five Championship hundreds in his first full season with Worcestershire in 2016 after becoming the first teen called up by the Lions since a certain Joe Root.
Haseeb Hameed will return at some point too and, while it is unlikely all of the next generation will be selected now, Bayliss wants an injection of youth.
"You need an opportunity to put them in and is this that opportunity?" he said. "Have the guys who are in there done enough to warrant further selection? Over time you want new players not just putting pressure on but getting chances."
Meanwhile, leg-spinner Crane should play the fifth Test on a ground known for taking spin. But whether he will replace the out-of-form Moeen Ali remains to be seen as England are still worried about the balance of their side without Stokes and Moeen and the length of the tail.
Curran could be the man to make way if England pick both spinners.
"There's no time like the present to find out if Crane is ready," added Bayliss. "He's a guy who's got the goods and the more he plays at this level, the better he will get."
There are not many better places for Crane to start than at the SCG.
England - New Zealand fixtures:
1st ODI: February 25, Seddon Park, Hamilton
2nd ODI: February 28, Bay Oval, Mt Maunganui
3rd ODI: March 3, Wellington Regional Stadium
4th ODI: March 7, University Oval, Dunedin
5th ODI: March 10, Hagley Oval, Christchurch
1st Test: March 22 - 26, Eden Park, Auckland
2nd Test: March 30 - April 3, Hagley Oval, Christchurch