Man United sealed the £75m signing of Lukaku from Everton earlier this week, with the Belgian becoming the club's second summer arrival following Swedish centre-back Victor Lindelof's move from Benfica.
Lingard has revealed that both Lukaku and Lindelof "have settled very well" with their new teammates, and the England international has said that the former has already shown his physical attributes during the early stages of pre-season training.
"Yeah they have settled very well, it's an easy squad to integrate with. Romelu and Paul [Pogba] are very close," Lingard told reporters.
"Romelu has settled in well, we know what he can do with the goals he scores. If he can bring that here it would be a big help. Romelu is very strong and physical and I think he will cause defenders problems this season, we've seen it in training."
Man United, who landed the Community Shield, League Cup and Europa League during the 2016-17 campaign, will open their pre-season tour of the United States against Los Angeles Galaxy on Saturday night.