Paine quit his disgraced test captain job last week over a landmark texting scandal, but is keen to keep playing.
Coaches must decide whether to let him go and start over or show loyalty amid a surge of support to keep him in the squad for the first clash in Brisbane on December 8.
Opener Marcus Harris said on Wednesday Paine had the backing of the Australian team and Lyon – who are one wicket from claiming 400 test scalps – reiterated it.
“The coaches have always said they are going to choose the best XI available and in my eyes Tim Paine is the best goalkeeper in the world,” he said. “I know I want it.
“Each bowler’s relationship with (him) is exceptional and Tim Paine is a very lovable guy and a very respected guy in the locker room.”
Lyon added that he could “100% guarantee that he (Paine) has the full support of the Australian dressing room”.
“Tim made a mistake, he admitted it, to me that shows great courage, to be honest.”
Paine resigned before a series of obscene text messages with a colleague in 2017 went public.
He was investigated at the time and was cleared of any breach of the cricket code of conduct, but said he was stepping down as skipper because his actions “did not meet the standards of ‘an Australian cricket captain’.
His replacement has yet to be announced with Pat Cummins and Steve Smith leading the pack.