The Brazil international suffered the injury in the opening minutes of Sunday's Premier League draw with Manchester City at Anfield.
It is a fresh blow for the 25-year-old, who had won his place back in the
Rodgers said: "It is very unfortunate. He has worked ever so hard to come back and he has been an outstanding player for me and person off the field as well.
"The indications are two to three months. It is quite a unique injury at the top of his right thigh.
"He has had a scan and we will see a specialist this evening. We'll see if it needs an operation or whether it is just recuperation."
Lucas lasted just four minutes of Sunday's 2-2 draw with the champions after first tweaking his thigh during the warm-up.
He had hoped to establish himself in Rodgers' new-look side after missing seven months of the last campaign with cruciate ligament damage.
The player himself tweeted: "No words describe my feelings at the moment. It is [sic] been hard to be positive but I am sure better days will come. YNWA."
Lucas' injury could allow an opportunity for new loan signing Nuri Sahin, brought in on a one-year deal from Real Madrid, to make his debut against Arsenal this weekend.
The Turkey international is ineligible for the Europa League qualifying round play-off second leg against Hearts.