Following Joshua’s defeat by Andy Ruiz Jr on 1 June, LeWIS questioned whether the Briton was fully prepared.
He also tweeted that Joshua’s trainer Rob McCracken may not offer all that is needed to “rule” at heavyweight.
“Lennox is a clown. I don’t respect Lennox,” Joshua, 29, told Sky. “Me and Lennox are cut from a different cloth.”
Joshua said he chose to “enjoy” and “appreciate” the next generation of fighters coming through, adding: “Lennox isn’t like that.”
LeWIS responds as Ruiz Jr wades in
The strengthened reputation of the WBO title has led to present-day fighters seeking four major belts to claim the same ‘undisputed’ description.
In his interview with Sky Sports, he said he was no longer “worrying about undisputed”.
LeWIS tweeted: “He’s right! We are cut from a different cloth. Undisputed wasn’t something I ‘worried’ about. It was something I went after until it was accomplished!
“Disappointed in AJ’s words but I understand that this ‘jealousy’ narrative was only fabricated after I criticised them for Wilder negotiations. All of the sudden I’m a hater.
“Ask who benefits from such a simple-minded narrative? Not AJ. Not me.”
The debate between the two former world champions has prompted plenty of reaction on Twitter – and when one account asked who would win in a fight between the pair, unified world heavyweight champion Ruiz replied: “Lennox all day.”
Joshua and Ruiz are at a stand-off in negotiations for a proposed rematch in SAudi Arabia on 7 December.