The 30-year-old has hit four goals in his first five Premier League appearances and the Toffees' boss claims he was monitoring the striker before his 2009 move to Southampton
Lambert will line up against the Toffees when the Saints travel to Goodison Park on Saturday and Moyes is well aware of the threat posed by the 30-year-old.
"He was in my attention when he was at Bristol Rovers," he told reporters. "Round that time we were looking around the leagues to see and we took Jermaine Beckford when Rickie was just about to go to Southampton.
|LAMBERT LASTING THE PACE|
|10/1||Rickie Lambert is 10/1 with bet365 to score the last goal of the game when Southampton face Everton on Saturday|
"We were well aware of him and his goalscoring and he has done great."
Moyes has continued to track the progress of the striker during his time at St Mary's Stadium, and the Scot was full of praise for Lambert and the work ethic that has seen him move up through the divisions.
"It is great credit to the boys who come through the leagues - it shows a great deal of hunger and perseverance to get through to the top and Rickie's done that," Moyes added.
"You can get released and it does not mean it is the end. What you have to do is go away and work at your game and what Rickie has done over the years is keep scoring goals wherever he has been.
"He deserves credit from working his way up from the bottom to the top."