Lukaku joined Manchester United from Everton for £75million in July and scored on his debut against Real Madrid in the European Super Cup on Tuesday.
The Belgian scored 25 goals for the Toffees last season, only second behind Tottenham’s Harry Kane in the race for the Golden Boot.
But Neville still has question marks over him having watched him closely since his arrival in England in 2011.
“My question marks over him having watched him for the last couple of years are in big matches at sometimes I don’t think he has done enough,” Neville said on Sky Sports.
“You could argue Everton don’t get the service into him, and also which is important is work-rate and work ethic.
“There is a school of thought that he should conserve his energy for the important bits which are further up the pitch.”
United drew 10 games at home last season, often against sides who finished in the second half of the Premier League table.
Neville says Lukaku must be the difference between Jose Mourinho’s men drawing and winning games at the Theatre of Dreams.
“The big thing is games like today where United struggled last season, where they were inadequate, they fell short, they drew 10 games here at Old Trafford, 0-0, 1-1, couldn’t break teams down, couldn’t get that goal, weren’t clinical enough,” Neville added.
“They had so much possession, I know there’s been a lot of talk about Jose Mourinho’s style but they dominated a lot of games here but just couldn’t kill teams off.
“He has to change those games, he has to be the difference in those games, he has to be the one that scores that goal, that turns those one points into three points.”
United start their league campaign against West Ham this afternoon (4pm) with Lukaku set for his domestic debut for the club.
Other new signings Victor Lindelof and Nemanja Matic are also set for their Premier League bow for United.