Lukaku has always been better for the Serie A rather than the Premier League. We have proof for that considering his past statistics.

Therefore Chelsea just signed him back for nothing. They were just fascinated with his performance at Inter and forgot about their past with him. It should be due to acting amateurish otherwise there is no way you do this.
Anyway he has returned to Italy but this time to Roma. It is a one-year loan deal though so I can't say good riddance for Chelsea. They will still have 2 more years with him in case he returns.
But let's say Roma didn't want to extend his loan and he didn't get any other reasonable offer in Europe then Chelsea can go for Saudi Arabia option for him.
I think Lukaku should go to Saudi Arabia and end his career there because I don't think any teams will want to sign him in the premier league, laliga, or serie A because every team doesn't see him as a good person. Lukaku's performance looks very good when he performs in serie A because even his performance was one of the things that led inter Milan to the final stage of the champion league last season. The fact that he contacted other teams to offer them a sizable sum of money in exchange for playing for them is not a bad thing in my opinion, however. He is a player and deserves the best for himself, and even though they perceived him as a traitor, they did not treat him that way.
In my opinion, Inter Milan is also a traitor because he used every means possible to support the squad last season and wanted to sign with them despite not having said that he would play for them again. Because I don't think inter Milan have an attacking player who can compete with Lukaku, I believe inter Milan will be aware of what Lukaku did for them last season. As Roma sign him on a loan from Chelsea, I believe he will perform well, and even if Roma don't want to sign him permanently, Saudi Arabia will sign him next season.