The Brazilian, who missed most of last season after knee surgery, has been ruled out for two to three months with a thigh problem.
New boss Rodgers is confident, after seeing the player's response to last year's troubles, that he can return to action closer to beginning than the end of that timescale.
Rodgers said: "He's quick healer so I would hope we would have him back quicker than that but we won't be rushing him.
"It is unfortunate he had got over his knee problems and was looking strong, getting near to full fitness and then he's had this.
"We are hoping that is a maximum. He is a very courageous guy and very focused. His aim is to get back as quick as he possibly can."
Lucas tweaked his thigh in the warm-up prior to last weekend's Premier League clash with Manchester City at Anfield and lasted just four minutes of the game.
It came as a major blow to the 25-year-old after missing seven months of the last campaign with cruciate ligament damage.
Lucas had been hoping to establish himself in Rodgers' new-look side after being handed a starting chance alongside
The player himself wrote on Twitter: "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' prognosis was confirmed after a scan on the injury but the course of his treatment is still to be determined.
Rodgers said: "It is extremely 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' injury could allow an opportunity for new loan signing
English Premier League
If you are going to achieve something as mad as spending nearly 27 years in the biggest job in football, you might as well bow out in equally ridiculous fashion.