The 32-year-old completed a switch to Anfield, where he previously served as a trainee, from Southampton on Monday.
A boyhood Liverpool fan, Lambert has admitted he did not expect to get another chance to play for the club.
However, he is certain he has what it takes to shine under manager Brendan Rodgers, having previously risen through the English divisions with Southampton.
"I am more than confident that I will take the chance and I will be able to improve my game again. I've done that every season," Lambert said.
"I'm going to get fitter. I'm going to do everything I can to get onto the next level now.
"Even though I'm 32, I feel like a kid again."
A prolific scorer in the lower divisions for Southampton, Lambert went on to score 28 goals in two Premier League campaigns with the club.
He was rewarded with a maiden England call-up last year and went on to earn a place in his country's FIFA World Cup squad.
Lambert credits Mauricio Pochettino, who recently resigned as Southampton boss to take over at Tottenham, as a key figure in his development.
"Everything went my way at Southampton and each manager that came in improved me massively and especially Mauricio," he added.
"He taught me how to be a different kind of player and I think that's helping now.
"I never really got taught to be a striker in the first place and then I never got taught how to be a lone striker. He taught me how to be the lone striker."
