Lambert, who as a teenager had a job putting lids on jars of beetroot, already has top scorer gongs from the Championship and Leagues One and Two.
He said: "I am still pinching myself. It's been an unbelievable rise and a great couple of years.
"I've always dreamed of scoring in the Premier League. It's been a long, long road, but I always said I had the ability to play at this level.
"I've had some big lows in my career but also some big highs.
"I am enjoying every moment, every game and every stadium I am going to. I don't set any sort of goals target and it's not something the manager Nigel Adkins does, either.
"I will aim to go out and contribute as much as I can in every game, not just scoring goals but bringing people into the game. Everton is a game all the lads are buzzing for and, as a Scouser, it is one I am definitely looking forward to.
"I grew up as a Liverpool fan and all my family are massive Reds, so they are desperate for me to beat them."