The Belgium international made a switch to United from Everton before the start of the 2017/18 season. He had a good start to his Old Trafford career, 11 goals in 10 appearances in all competitions.
However, Lukaku has struggled to find the back of the next since October. The striker has managed only one goal in the last 11 matches. Jose Mourinho has backed the ex-Chelsea man, despite his poor goalscoring run.
Jose Mourinho's side will face the north London club and Pep Guardiola's men in the next two fixtures. The trip to the Emirates will be on 2 December followed by the Manchester derby at Old Trafford on 11 December.
Neville wants Lukaku's overall contribution to be "big" against the top sides. The former United defender also stressed the 20-time English champions will need him to impress in "big matches".
"I don't think Jose Mourinho will be worried about Romelu Lukaku's lack of goals, but I think ultimately he's got two big games coming up," Neville told Sky Sports.
"He was brought in to score goals in the games which United were drawing last season. However, it is in the big matches where they now need him most. If there is a way to get at Arsenal and Manchester City then it is by really going at their defences.
"For a striker, it is all about your goals and unfortunately, people will always measure him by that, but away from the goals his contribution has to be big, to mess their centre-halves about.
"He's had his struggles but ultimately that was always going to happen at some point after his blistering start, but this is a critical stage of the season where he has to deliver."