Lucas suffered the problem just 20 minutes from coming on in the second half in Saturday's 2-2 draw at home to Aston Villa following a challenge with Fabian Delph.
It is understood that the 27-year-old Brazil midfielder has damaged the ligament in his right knee.
The news comes as a blow to Reds boss Brendan Rodgers as he looks to guide the Anfield outfit back into the UEFA Champions League with a top four finish in the Premier League.
Rodgers has been using Steven Gerrard in a more defensive midfield role recently and is confident it is a position his captain can operate in.
The Northern Irishman was hopeful Lucas could return ahead of schedule and 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."
When asked if the injury would affect Lucas's chances of representing hosts Brazil at this summer's World Cup finals.
"I'm sure Luiz Felipe Scolari will have a real good idea of who he is going to bring anyway and I don't think this injury for Lucas will deter that," Rodgers added.
"They've got their last squad get together in March. He was in the last one and I'm sure he impressed.
"They've got a big pool to pick from there, a lot of players, but I'm sure he has an idea of who he wants to pick already."