The 26-year-old, who tried to orchestrate a move away from Merseyside during the summer transfer window, made his Premier League return from a 10-match ban against Sunderland on Sunday.
The Uruguay international marked his top-flight comeback by netting two goals in the Reds' 3-1 win over the Black Cats.
"He is a world-class player and it is so important to have players like that if you want to fight for good things this season," Lucas told the club's official website. "Hopefully he will have another fantastic season for us like he did last year.
"Luis showed with his performance that he is really committed to the team and to the club. He just wants to help us, and we will try to help him too."
Following their victory at the Stadium of Light, Liverpool have moved up to second in the league table.