Lukaku scored his third goal for United in his second game but former Crystal Palace boss Alan Pardew thinks he can still improve his movement.
Pardew said he can learn from the likes of Ruud van Nistelrooy and Teddy Sheringham and adapt his game to become a more complete striker.
"Lukaku for me needs to improve at Man United when they regain possession," Pardew told Sky Sports after the game.
"His movement today wasn't good enough, to come short or to go long. To make it quicker action, he needs to get a little bit more of that and he'd have got more touches today.
"There were times when the ball changed hands to Man United and he was static or behind the centre back, he needs to think a little bit quicker. Obviously when the chance comes this guy doesn't miss.
"We were talking about (Ruud) Van Nistelrooy and Teddy Sheringham, and Zlatan (Ibrahimovic), he needs to get some of that, to get some of that cleverness on where to be.
"He's at the best place to learn it, he's going to be watching the videos with Jose (Mourinho) after the game and his coaching team and they'll be telling him to switch on a little bit quicker because once it goes into him - and he sticks it - wow."
Mourinho had admitted he is interested in re-signing Zlatan Ibrahimovic once the Swedish striker returns to fitness and Pardew believes Lukaku would benefit from his return to the club.
"I think one of the best things that can happen for him (Lukaku) at Man United is that they re-sign Zlatan, because I think he could learn so much," Pardew added.
"To see a player like that do it in training and to understand that close up will be a great learning curve for him, so I think it'll be a good move for them."