What do you mean?

That heritability doesn't cover all genetic factors. E.g. out of 100% of IQ variation 50% might be inherited, but that doesn't say that the rest is nurture, right? It can still have a huge factor of genetic lottery. E.g. isn't heritability the mean of the genetic effects, but there's also the rest of the distribution (std. dev)?

Still have no idea what distinction you are making.

"Heritability", strictly construed (as is the case in every study establishing heritability numbers) isn't necessarily a description of a "genetic lottery" at all. Plenty of things are highly heritable and not at all genetically determined, and the converse is also true!