Lukaku is clearly a difficult character but his representation also seems very poor. I don't think Lukaku ever really wanted to leave Inter. He was successful and loved there in a way he has never been at his other clubs. But Inter needed money and my bet is that his agent pushed him hard to agree to the move to Chelsea. His agent is a third tier player. After Lukaku, the most valuable clients at his agency are Demarai Gray and Neal Maupay. Moving Lukaku for 100m is basically a once in a career opportunity to bank a huge fee for an agent like that.
Lukaku, for his part, is kind of a thin skinned narcissistic man child. So after he shows up in London and realizes that the grass isn't greener despite the salary being larger, he immediately starts angling to get back to the only club that ever really made him feel wanted.
I have no idea what Chelsea will do but I think they're firmly in the realm of cutting losses and looking for the least-bad solution. Certainly the more that comes out about Lukaku's behavior and his desire to get back to Inter, the less likely it will be for some other club to enter the picture and offer a substantial fee for him. That already didn't seem on the cards given his age, wages, and recent performance. But why would anybody want to buy him if six months later he could start doing the exact same thing, angling for a move back to Milan?