The Belgium international completed a £75m move to the Red Devils from Everton last month after Manchester United saw off competition from Premier League champions Chelsea for Lukaku.
The 24-year-old will be tasked with filling the goal void left by club captain Wayne Rooney and Swedish legend Zlatan Ibrahimovic in all four competitions this season.
Lukaku scored 25 times in 36 games in the Premier League last season to finish as the division’s second-highest goal-scorer behind Tottenham Hotspur striker Harry Kane.
Manchester United’s new signing has faced questions about his big-game mentality following his lucrative move to the 20-time English champions.
However, Champions League winner May is under no illusion that Lukaku will prove a big hit at Manchester United and bring some different to Jose Mourinho’s team.
“Romelu Lukaku gives us a different dimension,” May told BT Sport.
“He’s very quick and very strong and he can bring people into the game.
“I would be very surprised if he did not get more than 25 goals this season.”
Lukaku scored 53 times in 110 games in the Premier League during four seasons at Goodison Park.
The Belgian forward moved to Everton in a £29m deal from Chelsea in the 2014 summer transfer window.
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