The 31-year-old could make his debut for the Three Lions in a friendly against Scotland next week, and Adkins believes that the forward's hard work has paid off.
"I think it's fantastic news for him," Adkins told Sky Sports News. "I'm absolutely ecstatic for him. Rickie just shows that if you persevere and work hard, [you] get the opportunity.
"It's great for him. He scores goals, he contributes, he assists. I really hope he gets on the pitch and goes on and scores."
Lambert worked under Adkins during the coach's time at Southampton.