Now 34, Gerrard's contract at Liverpool is set to expire at the end of the current season.
The midfielder is in talks with the club over a new deal and he was in the spotlight at the weekend after manager Brendan Rodgers rested him to the bench for the 1-0 Premier League win over Stoke City.
Gerrard - who has made over 600 appearances for his beloved Liverpool - was back in the starting line-up for Tuesday's trip to Leicester City, though, playing a starring role and scoring the second goal in a 3-1 victory.
With speculation continuing to mount regarding his future, Lambert believes Gerrard should see his career out at Anfield.
"I think I am speaking for everyone involved in Liverpool that we are desperate to keep Stevie," said the Liverpool striker.
"It's clear that it's his decision and the club's decision but I think he needs to stay at Liverpool for the rest of his life - that's my opinion.
"Stevie is his own man, but he is Mr Liverpool. I am enjoying playing with him, very much so, after years of watching him - and long may it continue."
Gerrard's own form has been closely scrutinised in recent weeks, but Lambert has no doubts over his quality.
He added: "I think some of the talk is silly, he was always going to come good, as he showed at Leicester.
"He has got more than enough in the tank. He is still one of the best players around for me.
"Obviously he is not going to play every single game but he showed what he can do."
