I would use the underlayment required by the LVP manufacturer as their product warranty will only be in effect with the underlayment they require.

There is no such thing as a dry sauna. Even with an IR cabin you can be dripping sweat on the floor. With a sauna you throw water on the stones to create steam, you typically sweat much more than with an IR cabin, and with IR cabins and saunas you need to wash the benches which results in a good bit of water on the floor.

Saunas and supporting areas are generally considered wet areas. You shower, go to sauna, rinse off in the shower, go outside to cool down, rest, repeat.

So for an interior space like this tile flooring built like a WC is often the best option.

Also, attics can be poor locations if they don't allow easy wet access to outside. Something to think about before investing a lot of money.

More:

https://localmile.org/trumpkins-notes-on-building-a-sauna/

https://saunologia.fi/in-english/

Does wine cellar look completed no refrigeration.

Saunas and supporting areas are wet spaces. You need to be able to shower > sauna > shower > go outside to cool down or jump in a cold plunge > rest > repeat.

That area does not look like it would be a good location for a sauna (and the tile looks like it'd be slippery when wet).

More:

https://localmile.org/trumpkins-intro-to-sauna/

https://saunologia.fi/in-english/

Thank you so much for all the great help!

What are you thinking for the sauna?