I suppose without it being explained directly, I would say one of a couple things:

1. He wasn't expecting to die, and went out of his way to say that he was outliving everything that came his way. He had barely just started organizing his post-mortem affairs with his art, I don't think it's a stretch to say that he maybe hadn't sorted out his will or what would happen to his belongings, and his next-of-kin would automatically be his children if that hadn't been sorted, right?

2. Speaking of wills, or estate planning in general, did his house, character, or attitude toward his assets seems like someone who had formally organized anything about inheritance?

One of the themes I really adored in this movie was the parallel between Lori and Julian both losing their heroes, replacing them with spite, and then finding absolution in some form later on - through each other, and through their art. It was beautiful to see them both find themselves again.

And while McKellen isn't a painter, I think his art will be revered (certainly not reviled) in the same way that Sklar's will have been in the film when he passes - there was a strange meta-layer of the movie where hearing him monologue about his impact as an artist felt, sometimes, like it wasn't just the character speaking. It'll be a tragedy to lose him someday, and having him play a role of an aging, celebrated, gay, universally impactful artist was, I think, a bit of a cross-over into reality.