Lewis, a Hall of Famer and a former undisputed heavyweight champion, has been critical in the past of Joshua's career decisions and in-ring performances.
Back in June at Madison Square Garden in New York City, Joshua suffered the first defeat of his career when he was dropped four times and stopped in the seventh round by heavy underdog Andy Ruiz.
During an on-demand special for Sky Sports, Joshua hit back.
"Lennox is a clown. I don't respect Lennox," Joshua said on AJ: The Untold Truth.
"Me and Lennox are not the same. My legacy is to sit back and enjoy the younger generation coming up, and not to be involved. Just to appreciate what it takes to get there. Lennox isn't like that. Me and Lennox are cut from a different cloth."
Joshua even shot back when it was discussed how Lewis left an impressive legacy - which prompted the once-beaten fighter to state: "So? So am I."
Lewis himself was shockingly upset twice in his career, with unexpected defeats at the hands of Oliver McCall and Hasim Rahman. He avenged both of those losses.
Joshua will attempt to avenge his loss to Ruiz, with a planned rematch on December 7th in Saudi Arabia.
Should be defeat Ruiz, then Joshua will focus on becoming the undisputed champion.
"I became heavyweight champion, I unified the division twice, and now my goal is to become two-time heavyweight champion of the world. Once I achieve that, I can look at becoming undisputed champion," Joshua said.
"That undisputed stuff? It was right in front of me but it was one of the biggest curses lingering over my head when I was champion." SHARE THIS NEWS USING ANY OF THE BUTTON BELOW PLACE YOUR TEXT ADVERT BELOW ⬇⬇⬇