Of course, there is a good bond between Lukaku and Mourinho. Lukaku may get a permanent contract with Roma. But what is also a problem is that Mourinho's contract at Roma will not last long. and if that is not renewed by Roma, then they will also have to adjust to a new coach.
but I still hope that Mourinho will remain in Rome with a squad that will hopefully get extraordinary improvements.
You're right. Lukaku and Mourinho have a good relationship. As long as Mourinho has a contract in AS Roma, no doubt Lukaku will stay there. Lukaku also will have a chance to sign permanently by AS Roma management. Unfortunately, it seems impossible because Mourinho probably leaves AS Roma after this season ends. So, we can assume Lukaku will be back to Chelsea and wait for an offer for his next destination club.
I think Mourinho has no intention to stay in AS Roma, he has a bad relationship with the players and AS Roma management lately. I think Mourinho will move to another league. He probably moves to EPL or SPL, depending on which offer is interesting. If he wants to get a new challenge and higher salary, he is likely to move to SPL.