Former England boss Glenn Hoddle said the player looked like he had been "dragged off the street" when he was introduced to the crowd at half-time during Saturday's 4-1 FA Cup victory over Brentford at Goodison Park.
New Everton boss Lampard, however, wants players to be themselves and express their individuality.
"I've heard some of the reaction and I have a lot of respect for everyone who has spoken, ex-players, people who I respect and admire in Ally McCoist, Alan Brazil, Glenn Hoddle -- I would never go against their word," said the former Chelsea manager.
"But when you are working closely with players and working with Dele, my personal opinion is that I don't care what car he drives, what clothes he wears, as long as I get a lad that comes to training every day, wants to improve every day, respects the club, respects his team-mates and then produces and gives everything to produce."
He added: "Everyone has their own individual personality and to try to handcuff or restrict that I think could be detrimental."
Both Alli and loan-signing Van de Beek will be in the squad for the first time on Tuesday, having been cup-tied on Saturday, as Everton travel to Newcastle for a crucial game against their relegation rivals.
Alli, who signed for Everton from Tottenham on transfer deadline day last week, was a member of Gareth Southgate's 2018 World Cup squad but struggled under a succession of managers at Spurs and fell out of the England reckoning.
Van de Beek has joined Everton on loan from Manchester United, where he has made just four Premier League starts since he joined them from Ajax in 2020.
Striker Dominic Calvert-Lewin also returns after a knee problem but defender Ben Godfrey has been ruled out for up to five weeks with a hamstring injury.
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