Lillis, 23, has made 24 appearances for Dale since joining them at the start of the season.
He will remain at Spotland until February 6, although the Iron can recall him at 24 hours notice.
"I'm pleased to have extended my stay. It's a great place to come to work and I'm looking forward to the next month," he said.
"I don't know what will happen after February 6, but there is a 93-day ruling on emergency loans so I could only stay until the beginning of April at best."