Upvote:2
Some of the public laundries in Lviv I just googled:
You can google maps for word пральня yourself and try to find something close to the place, where you stay.
Upvote:3
A quick Google search ("lviv laundromat") found several dry-cleaners, and this:
BUBBLES/Бульбашки 117 Volodymr Valeeki Str., Lviv
Come visit Ukraine’s only full-service Laundromat. Brand new American equipment. Do your laundry yourself or let our happy workers take care of all your needs.
According to them, they're the only ones. I doubt that's true, but there's at least one place to go.