Lambert joined the Reds earlier this week before linking-up with England for the World Cup.
The 32-year-old, who was playing in League One for Southampton as recently as 2011, has vowed to seize his chance at Anfield.
"I wasn't expecting a chance at Liverpool but I have got it," he said.
"Now that I've got it I will do everything to not let it go and 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.
"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. I've got so much enthusiasm for the game.
"The fact that I'm playing under Brendan Rodgers and for Liverpool I just can't wait.
"It could have come earlier in my career - if it had I don't think I would be performing at the level I am now. I might have missed the chance.
"This is a good time because I am mentally and physically ready. If it doesn't work out now there are no excuses.
"I have done everything I can to get to this point. I wasn't expecting a chance to play for Liverpool but now I've got it I'll be trying my best to deliver."