The 21-year-old has recovered from injury to feature against Queens Park Rangers and Burnley in the last two matches.
"He is going to have a massive future in the game," Lambert told Sky Sports News. "I thought he was very good against Burnley.
"For 21 years of age he has slotted in seamlessly as if he has been here for years and years.
"I am delighted with Dani. It is great for him at his age now to be getting regular first-team football and becoming more comfortable playing in front of big crowds."
Ayala joined the Canaries during the summer for a reported £800,000.