The Iron's first choice keeper, 24, has torn a knee capsule and damaged his posterior cruciate. He is not expected to return until December.
"Thank you all for your kind messages. Going to get my head down and work as hard as I can to come back stronger," he wrote on Twitter.
Lillis has featured in all nine of the Iron's competitive games this season following Joe Murphy's departure to Coventry City on a Bosman transfer.
He suffered the injury during Saturday's 1-1 draw with Colchester United at Glanford Park.
Alan Knill, the Iron manager, will add another keeper to his squad on a loan basis as Sam Slocombe is the only fit keeper currently on the books. Jake Turner, the Iron's third choice keeper, is on loan at Brigg Town.
That loan signing is expected to be Manchester United's youth team keeper Sam Johnstone.