And the rookie keeper pulled off a string of magnificent saves to deny the home side and leave them just three points off the bottom of League One.
A mistake from Richard Hinds on the half-hour allowed Darren Byfield in for the first real chance of the game, but the powerful defender recovered well and was able to block the former Gillingham striker's shot.
Filipe Morais came close five minutes before the break when his excellent free-kick was tipped over by Lillis. The youngster did even better to save Poul Hubertz's close-range header from the resulting corner.
As the half drew to a close Lillis was off his line quickly to deny Hubertz again when the giant striker found a yard of space at the back post, but couldn't get his shot off in time as Millwall failed to make the most of their dominance in the first half.
As the home side continued to search for the winner Steve Torpey came off the bench to earn all three points for Scunthorpe.
The super sub slid the ball past Lenny Pidgeley's goal from six yards after good build-up play from Andy Keogh and Marcus Williams.
Keogh almost made it two in injury time when he hit the inside of the post and the ball bounced clear.