The midfielder sustained the problem during the Reds' 2-2 draw with Manchester City at Anfield on Sunday and the boss explained how the Brazilian will visit a specialist on Wednesday evening in order to establish whether he needs to undergo an operation.
"Lucas picked up an injury at the weekend which was extremely unfortunate because he has worked ever so hard to come back [from injury]," Rodgers told reporters. "He has been an outstanding player for me and an outstanding person off the field as well.
"It looks like he's going to be out for a few months — the indications are between two to three months.
"It's quite a unique injury at the top of his right fem [femur]. He's had his scan and he will see a specialist this evening and we'll see whether he needs an operation or whether it's just recuperation and we'll see how that evolves from there.
"He's a quick healer so I'd hope that he would be back sooner than that. We won't be rushing him. He's worked terrifically well and it's unfortunate that he's got over his knee problems and he looked strong and somewhere up to near fitness and now he's had this injury."
The manager explained how he had spoken to Lucas after the player was given the results of his scan and that while the midfielder was disappointed with the news, he will focus on getting back to fitness as soon as he can.
"I had a good long chat with him," said Rodgers. "He went for his scan and then he got the news last night. He's obviously disappointed because he's worked so hard but this will be an opportunity and a chance for him to work on other areas.
"One [will be] to make sure that the strength in his knee continues to improve. He can still do some work off the field as well and it gives him a chance to focus. We are hoping that the [three months] will be a maximum.
"At this moment he's disappointed but he's a very courageous guy and he's focused. So his aim now is to get back as quick as he possibly can."
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