The striker netted a hat-trick at Anfield on Saturday to help the Reds to a 4-1 win over West Bromwich Albion, and has returned from his 10-match ban in scintillating form.
The Uruguayan was strongly tipped to join Arsenal in order to play in the Champions League during the transfer window, but Lucas is delighted that Suarez is still a Liverpool player.
"It shows why the club fought so hard to keep him in the summer," Lucas told the Daily Star. "What he did last year for us and what he is doing already just shows that is why the club wanted to keep him.
"Liverpool want to keep their best players and he was the best player last year - and probably the Premier League's best player. We are happy he stayed with us and he is just showing every week how committed he is. It doesn't matter what was going on in the summer his mind now is just to help the team, to achieve great things and hopefully it will finish in a positive way in May.
"We see him every training session and we know he loves what he does and when he gets on the pitch he just tries to help, that is why we are so happy for him because he deserves what he is getting. I think every single player wants to play in the Champions League. No one wants to stay at home on Tuesday and Wednesday watching the TV and not playing in the big games. He is probably one of the top five best players in the world so he wants to be there and that is why he is so committed with this team because he wants to put Liverpool back in the Champions League - that is what we all want."
Liverpool sit third in the Premier League table following the win at the weekend.