Alli played no part in the Toffees' FA Cup triumph over Brentford but, along with loan signing Donny van de Beek, was unveiled to fans at Goodison Park at half-time.
Former England boss Glenn Hoddle said Alli looked like he had been 'dragged off the street' when he was presented to the crowd during the break.
Meanwhile, the former Tottenham midfielder was the topic of debate on the talkSPORT Breakfast, as hosts Alan Brazil and Ally McCoist suggested Alli sent the wrong message by turning up for his first Everton training session in a Rolls Royce.
Ex-Spurs striker Brazil said on the talkSPORT Breakfast: "A thing that annoyed me… well, it didn't annoy me, I want to see the guy play football again, but Dele turns up in his Rolls Royce and - maybe I'm old fashioned - but I'm like, 'oh no, Dele, don't do that'.
"It's just little signals like that, to me… am I wrong, Ally?"
"Listen Al, I don't think you're wrong, I definitely agree with you," replied the Rangers legend. "But we are of a completely different generation, that's the one thing we do have to accept."
Brazil added: "I'm not saying he should turn up in a ten year old Skoda!"
"I know," said McCoist. "Wee things like that… I'm bursting for Dele Alli to do well.
"But Evertonians, the fans, they are working class people and I don't know if it sends out the right message. I'm with you Al, however, I do accept that we are of a completely different generation."
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 Lampard in his press conference on Monday, ahead of Everton's Premier League clash against Newcastle.
"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 teammates and then produces and gives everything to produce.
"The modern day has moved on, it's changed, we all have to be aware of that, and I'm not hitting back at any observation because everyone is allowed their own opinion but I can only deal with what is in front of me.
"And what I've just mentioned, that Dele and Donny are both great lads, I mean it.
"Maybe Donny wears an overcoat that is longer than Dele wears, and he has a different type of jacket, but it doesn't bother me.
"As long as they produce on the pitch then I'm very happy. Everyone has their own individual personality and to try to handcuff or restrict that I think could be detrimental."
That does not mean, however, that Alli - or any player - will be given free rein on the pitch.
Lampard has a specific way of working and while there is some room for individual expression, players have to follow the game plan.
"It's a different question to 'What coat is Dele wearing?'. It is more when you have a game plan, players have to have a discipline within that," he added.
"I am not a fan of absolute freedom, I think that is an easy way to coach - 'Go on lads, go and do it, express yourself' - there has to be a plan.
"But when you do get to the final third it is not for me to tell Anthony [Gordon] or Demarai [Gray] or Dele or Donny what decisions to take in that area. That is where you have to give a little bit of licence to those players.
"I'll always offer freedom within the structure of how we are playing but the structure of the team is really important for me, so the players have to buy into that first."
Both Alli and Van De Beek will be in the squad for the first time, having been cup-tied on Saturday, as Everton travel to Newcastle for a crucial game against their relegation rivals on Tuesday.
Striker Dominic Calvert-Lewin also returns after a knee problem but defender Ben Godfrey has been ruled out for four to five weeks with a hamstring injury sustained at the weekend.