Southampton pair backing Rodriguez for big impact
Lambert and Rodriguez scored 52 goals between them last season and were named as the strikers in the PFA's Championship team of the year.
And Lambert told the Saints website: "When I played against him last year I felt he was a very good player. He's a good, young English talent and I'm very much looking forward to playing alongside him."
Cork, who played alongside Rodriguez at Turf Moor, said: "I've heard that it was a lot of money but I'm sure Jay will justify the price tag because I know he's a great player.
"He's quick, he's strong, a good header of the ball, and he can score a variety of goals - not just inside the box, but a few outside as well."