Lulic underwent an operation on Wednesday evening after injuring the ring and middle fingers of his right hand while training in the gym, according to a Lazio statement on Wednesday, which gave no further details of the incident.
Reports on Thursday claim the Bosnian international will be out of action for up to a month and could be forced to have the top part of his ring finger amputated.
Lulic, 29, is one of Lazio's key players and despite scoring only once in the league this season will be missed in a crucial run-up to the Christmas break.
Lazio have taken only one point from their last five games, after managing to hold Palermo to a 1-1 draw at home a fortnight ago.
They welcome resurgent champions Juventus on Friday, when a win could, according to reports in the Italian media, cost Lazio coach Stefano Pioli his job.
Lazio sit in 10th place, six points above the drop zone and 12 points behind leaders Napoli.