Graham joined Championship outfit Blackburn on loan from Premier League club Sunderland in the January transfer window.
Now that the season is finished, the 30-year-old striker will return to the Black Cats, but he will become a free agent in the summer when his current contract with Sam Allardyce’s side runs out.
Lambert, who announced last month that he will leave Rovers when the 2015-16 Championship campaign ends (as reported by The Guardian), believes that Blackburn should sign Graham on a permanent contract.
“He’s scored seven goals for us and that’s a big return as he’s only been here for three months,” the former Aston Villa manager told The Glasgow Evening Times.
“My advice to the club would be to try and sign him. No two ways about it. But I don’t know what Danny wants to do. He has to be the judge of that.”
Graham has been linked with a move to Scotland in the summer transfer window, with Old Firm rivals Rangers and Celtic credited with an interest in the striker.
According to a recent report in The Sun, Rangers manager Mark Warburton has identified the former Swansea City striker as a summer transfer target.
It has also been reported by The Sun that if Brendan Rodgers becomes the new Celtic manager, then he will look to sign Graham with whom he worked at Swansea.
Graham scored seven goals and created 15 chances in 18 Championship appearances for Blackburn this season.