The 32-year-old secured an emotional return to Liverpool before heading to Brazil with England for the FIFA World Cup, where he is also captained by Gerrard.
And Lambert is relishing the chance to play alongside the Anfield skipper regularly next term, hailing his influence on all members of Brendan Rodgers' squad.
He told the club's official website: "He's still one of our best players - still world-class, in my opinion. As a deep-lying midfielder he's one of the best.
"And he's good off the field too - not one to shout.
"He does his actions on the pitch and he speaks to the young lads and puts an arm around them when it's needed.
"It was top drawer the way he walked off with Raheem Sterling when Raheem was sent off against Ecuador. The young lads aren't intimidated and he's one of the main reasons for that."
"Whatever decision he makes everyone is going to be behind him and respectful of it," added the former Southampton man.
"But, if you are asking my opinion, I think he can go on for a number of years."
