The well-travelled 31-year-old was handed his international bow in the Wembley friendly with Scotland last Wednesday and stepped off the bench in the second half to head home the winner with his very first touch.
Lambert, who then netted a last-minute penalty to secure victory over West Brom on Saturday, joined the Saints from Bristol Rovers in a £1million deal in 2009 and believes his current home gives him the ideal platform to showcase his abilities.
The former Macclesfield, Stockport and Rochdale man said: "I knew that it would mean a lot to the Southampton fans and the club to see one of their own involved with England. They've always backed me.
"I always thought my best chance of playing for England was with Southampton.
"I played in 38 games in the Premier League. I don't think there are too may England-qualified strikers who get that opportunity.
"But I'd never have thought about leaving Southampton to enhance my England prospects."