The much-derided 23-year-old was one of the more consistent performers last season but, as he is seen as being a favourite of former Reds manager Rafael Benitez, doubts have been raised about the Brazilian's future.
However, he is determined to prove to new boss Roy Hogdson he is worth a place in the squad despite being linked with Palermo.
"I'm happy in Liverpool and looking forward to my fourth season," he said.
"I hope I stay. I'm happy to play for Liverpool and to improve my performances, as I did last season.
"I'm not here to try to prove critics wrong. I'm here to prove myself to the manager and my team-mates.
"That's the most important thing. I don't know why people criticise me so much but I just try to be positive and be strong.
"I know I had a good season last season and hope it will be even better this season.
"I have to keep going and show the manager that I can play and have the quality that he expects."
Lucas is one of the few senior players currently at the club's training camp in Switzerland so has been one of the first to experience Hodgson's methods.
"He seems to be very good as a coach, good with the tactical side of the game," he added.
"He will help everyone but for me he has a lot of experience, he has worked with big players at big clubs so his experience will help in giving me advice to help improve my game.
"I am confident we will have a better season. When there are lots of changes new motivation comes through and I think we can do better. We will do better."
Meanwhile, Hodgson has confirmed Sammy Lee will remain at the club, although his exact role has yet to be decided.
Former Reds midfielder Lee was Benitez's assistant manager and has been told he still has a job among the backroom staff.
"Sammy will stay here for the foreseeable future, absolutely - as long as he wants to be here,'' Hodgson told the Liverpool Echo.
"I have no intention of letting him go and if he wants to stay with us, he is more than welcome.
"I haven't made decisions on any [other positions] yet.''