As far as I know (please correct me if I'm wrong), лазня in Ukrainian = парилка in Russian. If that is the case, then the correct English translation is steambath. A steambath is not actually a sauna.
Yes, so that confirms my theory! Will report next time I do this sentence.
For sauna (dry air) we say сауна. Лазня is with moist air which is same as баня in Russian.
I think that баня is more Russian than Ukrainian for лазня. Please correct me.