The Belgium international was sold by United to Inter this summer, with Neville critical of the forward because of his weight and apparent lack of fitness.
However, Lukaku has directly responded to Neville's assessment of him. In an interview with BBC Sport's Simon Stone, Lukaku said the pundit was incorrect to doubt his professionalism:
"He (Neville) can talk about my fitness but he should never say anything about my professionalism, that I don't work hard enough. That is something he cannot say. All the coaches I have had say the same thing about me.
"What did Ole Gunnar Solskjaer say when I was on the training ground? What did he say? That I always work hard and always do my best to try and improve myself. Same with Jose Mourinho and Roberto Martinez. Now Antonio Conte will say it.
"Last year was just a bad year. It happens in football. You just have to move on. I am not going to sit here and react in a negative way.
"We are grown men. He is a pundit. He gets paid to say this kind of stuff. I am paid to play football. I just want to do my best for Inter Milan. That is it."
Neville had questioned Lukaku's efforts in a tweeted response to football journalist Andy Mitten on August 8. The ex-United captain did not hold back and said about the player, "unprofessionalism is contagious":
Lukaku was clearly not the type of striker Ole Gunnar Solskjaer wanted at the start of his first full campaign as manager. The Norwegian favours a pacey No. 9, and will play either Marcus Rashford, Anthony Martial or Mason Greenwood through the middle. The presence of the three players in the squad made sure of Lukaku's departure.
The 26-year-old lasted only two seasons at Old Trafford after being purchased by Jose Mourinho. At Everton, Lukaku had plenty of service from the wing, but at United, Mourinho played a more narrow style, constricting the team's ability to spread the attack.
Lukaku scored 35 goals in two campaigns with United in the Premier League and Europe, proving his goalscoring was not the wider issue.
Solskjaer wants to play with a high press at a greater tempo, and the Belgian was entirely unsuited to this method.
At Inter, Lukaku is likely to feature in a more conventional striking role, and the reduced pace of Serie A could mean the player thrives in his new environment in Italy.