The Belgium international scored his first goal of the season in the Toffees' 2-0 victory over West Bromwich Albion on Saturday.
The goal was Lukaku's first since sealing a permanent move to Goodison Park from Chelsea in the summer, for a reported £28m fee.
"He wants to be the best footballer in the world, he really does," ESPN quotes Howard as saying. "That's what he thinks of himself. He gets his head down and he works, and we push him.
"He's electric, he's alive, he celebrates goals in training, everything counts to him. Everything matters. That's what you want to see. There are too many young kids that take it for granted. Romelu doesn't. He cost a lot of money but he is not arrogant, he is hungry."
Saturday's win was the first for Everton in this season's Premier League campaign.