The Brazil international lasted just 20 minutes as a second-half substitute in Liverpool's 2-2 draw with Aston Villa at Anfield on Saturday.
Lucas described hearing a "click" in his knee and reportedly left Anfield on crutches.
In a press conference at Melwood on Thursday, Liverpool manager Brendan Rodgers said: "First of all, personally, I am disappointed for Lucas because he's been very, very important for our squad this season.
"It was something that was innocuous really and has put him out for a few months.
"Hopefully he'll get back sooner rather than later. He'd been in good form this season and had worked his way back into the Brazil squad.
"Knowing what he is like, he'll be back sooner rather than later - and he'll do everything in his power to get back.
"In the meantime, that leaves us short of a really good player."
