The England international returned to action against Aston Villa on Saturday after missing the opening seven games of the Premier League season with a knee ligament injury.
Barkley assisted Lukaku's goal in the 3-0 win at Goodison Park, and the Belgian is delighted to be playing alongside the 20-year-old midfielder again.
"He is like a friend and brother to me off the pitch," Lukaku told Everton's official website. "I am very happy that he is back on it because he brings something that the whole team needs.
"He has that rawness, that skill, that power. He is a perfect partner for me to play up front with and I am very happy that he is back.
"There are loads of players who can help me, but he has something that none of us have. I can't explain it. He is the best player in our team. He will be somebody that the England team will rely on."
Everton travel to Lille in the Europa League on Thursday.