You have to take all the emotion out of it and look at the facts.
Does he have anything in writing to support his claim that your Aunt promised he could live in someone else's house for the rest of his life?
Obviously not because she did not promise that. She can't promise that, it's not her house. So he has nothing to back up his claim. That will be dismissed.
Is he a legal dependent of your Aunt?
He would need to meet the strict criteria. For example, look at visas. A person can apply for a dependent visa in most countries but they need to show proof ie they are a spouse (living together full time) or child of that person, or they are an adult with a disability. In court, in legal terms, he is clearly not a dependent so that will also be dismissed.
The truth is, this is not going to get as far as court because no legal team would take his case without significant costs paid upfront.
What they will try to do, and what you should be wary of, is get you to agree to 'settle out of court' ie give him money which I know you have already offered but if they are asking to settle it's because they have no case so there is no point giving him money. Put it towards your own legal expenses instead.
If he offers to settle, get your solicitor to reply to say that your previous offer, which he has already declined, is withdrawn due to the costs of further legal advice and no further offer will be made.
And that will be that. No court. No settlement. Just him gone.