Manager Roy Hodgson will soon be selecting his squad for next month’s friendly against Brazil, at Wembley.
Lambert has made a strong case for inclusion, with no English player able to better his ten Premier League goals this season.
Four of those have come in his last six matches, while he has also been credited with three assists this term.
At 30 years old, and only in the midst of his first top-flight campaign, Lambert has a lot of persuading to do in order to convince Hodgson.
But Puncheon believes the forward’s displays merit international recognition.
“For me, he definitely deserves an England call-up for what he’s done,” said Puncheon, who himself was tipped for a possible future England role by his former Barnet manager, Paul Fairclough, earlier this season.