Correct, Lukaku loan contract is about to end at the end of June, yes this month. As you said Lukaku last played with Inter is against Manchester City in final UCL and it was very disappointing, and I also think that Inter may not want to extend his contract. Although at the moment there is no official news regarding Inter and Lukaku, but I think Inter have a firm stance, the failures of this season will not be repeated in the next season.
Even pep has been commenting on failed heading by lukaku. His performance in the final was quite disappointing but stupid. simeone was letting him in 30 minutes before the game end.
It's a big mistake by him. It has been reported that if intermilan has no money to make lukaku as permanent transfer. It seems like that lukaku will be going back again to the chelsea soon. He has no choice and chelsea is not willing to give lukaku to the intermilan as a loan. Pochettino needs to trust him in this case since all of chelsea's strikers were leaving. Some are coming it like nkuku and jackson, probably lukaku will follow soon.
Intermilan is a poor club with huge debt now. it can't afford to buy lukaku from chelsea with permanent status.