The 23-year-old striker helped himself to a hat-trick in Monday night's 3-0 win over Sunderlandat the Stadium of Light to open his scoring account for the Toffees this season.
Lukaku had started the new campaign slowly before going away and netting a double for Belgium last Tuesday night and Koeman feels that assisted him in rediscovering his best for his club.
"The two goals with Belgium gave him a boost and it's unbelievable how good he can be and of course strikers love scoring goals," he told Sky Sports.
"He showed his quality, he showed the goals tonight, a great performance."
Lukaku headed home a stand-up cross from Idrissa Gana Gueye on the hour-mark, again headed beyond Jordan Pickford when found by a lovely Yannick Bolasie piece of play eight minutes later and wrapped it up when racing onto a through ball from Kevin Mirallas to coolly convert with his left foot on 71 minutes.