Miscanthus will not tolerate temperatures below -5 deg. C, so unless you can put somewhere inside during winter, it probably won't survive your winters.

Good choice. We have miscanthus giganteus here in France and it has withstood temperatures of minus 20C. I'm surprised by Bamboo's comment but perhaps this applies to young plants or wet soils..
It dies right down to the base at the end of the season though the huge plumes remain until the next spring when it begins to re-grow. The clump of stems seems to protect the roots without problems so don't cut them down. They provide the winter interest in any case.
Although they aren't terribly strong, the old stems are long enough and hard enough to tie between canes and string to make a structure on which you can grow beans or peas, or sweet peas.
You can cut up the stems to make stacks of stems which are ideal for overwintering beneficial insects like ladybirds or lacewings.
This is a super plant and I hope you are able to succeed with it in Lithuania.

Not speaking from personal experience Bertie, just reporting what the RHS Encylopaedia says!