"Steve underwent surgery on his sportsman's hernia yesterday afternoon and walked out of the hospital unaided later in the evening," Lions physio Bobby Bacic told the club website.
"In fact he was awake during the double procedure as he wanted to know the how we were getting on at Sheffield."
Bacic added that Morison's return to full fitness is unknown but that he could be back within a month.
"It is too early to give an exact return date as Steve will need to allow the operation sites to settle and avoid infection.
"However if there are no complications then a return to play within four weeks is a possibility. Steve will remain at our club for his rehab."