Okay, so imagine a big group of people who all live in the same place and speak the same language. This group is called the Lemko people and they used to live in a region called Lemkivshchyna, which is now part of Poland, Ukraine, and Slovakia.
A long time ago, when the Lemkos had their own country and government, they called it the Lemko Republic. But then some other countries took over their land and the Lemko Republic disappeared.
Nowadays, some Lemkos still talk about the Lemko Republic and want to have their own country again. But it's a complicated situation because the Lemkos live in different countries and some of those countries don't want to give up their land.
So, to sum up, the Lemko Republic was a long time ago when the Lemkos had their own country, but now they don't and some people want it back.