Does Apple watch 8 work properly in Lithuania if bought in USA?

It will work as a GPS only device. It will most likely not work on cellular networks outside of North America if it is a cellular model.

Some health features are regulated and will only work if used in a country where they have been approved for use by the relevant government health agency.

If you want a watch that works for cellular carriers in Lithuania, buy the watch in Lithuania, NOT the US.

Apple Watch - Carriers - Apple

You also get no Apple Support and no Warranty. That's a big financial risk to save a few Euros.