The 25-year-old is yet to make his international debut but was called up to Roy Hodgson's squad for the World Cup qualifier against Ukraine in September 2012.
"It's an ambition for the future," Lallana told BBC Radio Solent. "I've been playing with Rickie for quite a few years now and for him to be called up regularly is brilliant.
"I've got someone I'm playing with at the moment who is living the dream and I want to emulate him and what he has achieved. I'm delighted for him and the club."
Lambert has scored two goals in three appearances for England.