The Belgian striker has been an instrumental figure as Conte has guided the club to their first Serie A title since 2010 and admits that he appreciates the coach's honesty.
Lukaku told La Tribune: "I would fight to the death for him. I couldn't join him at Chelsea, but I always said I would play for him the day I left Manchester United.
"Conte told me very directly: ‘If you don’t work in training you won’t play, it’s essential that you know how to play with your back to goal.'
"It’s important to meet people who tell you the absolute truth to help you improve."
Lukaku believes this season has been the best of his career and wants to experience more success with Inter after the ended Juventus' long reign as Italian champions.
He said: "Last year was good too, but this was the best of my career.
"It’s wonderful and I hope to continue like this. I want to thank everyone, I am truly so happy."
Lukaku also expressed his relief after winning just the second major trophy of his career and is prioritising team success rather than individual acclaim.
He said: "I thought it was now or never. In a career you can score 500 goals, but if you don't win in the end it's all in vain."