Goodman Games

It says the katana in Frozen In Time functions as a longsword. Does that mean Warriors/Dwarves that have longsword as their luck weapon get the same benefit from it, or does it not apply, since the weapon has a different name? Thanks.

I say no.

Longswords and katanas are two different named weapons, although the katana functions as a longsword. If a luck weapon said "katana" they'd get the benefit from using a katana, but not a longsword.

This may be a disappointment, but it could also be a good thing, for instance, an unlucky warrior who happened to pick longsword for their "unlucky" weapon would thus not be penalized for using the Katana.