Speaking to Stile TV, Ledure said Lukaku had simply needed time to recover his best form after a campaign disrupted by fitness problems.
"Lukaku needed time, which is what he didn't have in the season just gone," Ledure said.
"He needed time to get back into shape and be competitive, and that's what's happened in recent weeks. He doesn't yet have 90 minutes in his legs, but he's back to a great level and can help the team."
Ledure said the cause of Lukaku's physical struggles last season remained unclear even to those close to the player.
"There were setbacks in the second season, and that didn't allow him to have the ideal medical and physical condition to be competitive on the pitch. I don't know the reason, but it happened. He just needed time, and we're all happy that he's now back to being competitive," he said.
Asked about the departure of head coach Antonio Conte from Napoli, Ledure declined to speculate on how Lukaku felt about the change.
"I don't know if Lukaku is happy or not about not finding Conte as Napoli coach. He has a contract with Napoli for another season, he likes being in Naples and playing for Napoli," Ledure said. "What might happen this summer we don't know — it depends not only on the player but also on the club. There's no point making predictions now, I don't want to anticipate what might happen. There's a World Cup to play, we need to understand how he plays and how he is physically. What happens after that, I don't know."
Lukaku endured a difficult campaign at Napoli last season, with the club's hopes of a strong Champions League run undermined in part by his fitness issues.
"Lukaku wants to win, he had big expectations for this season. He was also very happy to play with De Bruyne. He had the ambition to do well in the Champions League, but for reasons that didn't depend on his will, it didn't happen, and it didn't go as he and all the Napoli fans had hoped," Ledure said. "It was a disappointing season, but it wasn't anyone's fault in particular. In the end, people remember the players who win, not how much they earned. The only thing I can say is that you have to look forward."
Ledure was also asked whether he was satisfied with Napoli's choice of Allegri as Conte's successor.
"My opinion doesn't count for anything. I'll say that Lukaku has good relationships with a lot of people in football," he said.