The Belgian, who joined the Toffees on a season-long loan on transfer deadline day from Chelsea, has scored three times for the club in his first two appearances to help the Merseysiders climb to fourth in the Premier League table.
Lukaku netted a brace and bagged an assist as Everton edged out Newcastle United 3-2 on Monday night, and Jagielka admits that he doesn't envy defenders who come up against him.
"He's a fantastic acquisition for us," Jagielka told Sky Sports News. "He's a great player and has probably taken us up to that next level.
"If he can keep himself fit and keep himself confident, he could be great for us. He has all the attributes and he loves playing football, and if you put it all together, then it can lead to some interesting days on the training pitch for us defenders.
"He's a real presence up front. Obviously he wasn't quite getting the nod at Chelsea and that's made him even hungrier than he was last season [when the Londoners loaned him to West Brom]. He's definitely a handful, I try to stay away from him in training, to be honest!"
West Brom host Arsenal at The Hawthorns on Sunday.