The 22-year-old enjoyed a spell at Notts County last season and, despite his promise, Lillis is likely to find first-team opportunities hard to come by this campaign after first choice Joe Murphy signed a new deal.
"Joe made is clear he wanted to stay and we are delighted he has now agreed a new deal," Adkins told the Scunthorpe Telegraph.
"But people know how highly we regard Josh Lillis. I want him eventually to be in a position to take over from Joe when he does eventually leave.
"To do that, Josh needs to play some regular first-team football and that is what we will be looking to try and get for him this season. He benefited from a spell on loan last season and I am sure he will again."
Sam Slocombe, signed from non-league Bottesford Town last year, is set to be Murphy's deputy next season.