There are many public saunas (called pirties) in Lithuania. I have visited four of them, but there are more.
Here is the list of public saunas probably working in Lithuania outside of Vilnius and Kaunas. If you know any details like address or opening hours, please, tell me.
Panevėžys: Ukmergės g. 31
Klaipėda: Trilapio g.