Identify old Lithuanian board game
From your description, it sounds like you're describing the game-board for Qirkat, which is a precursor to Checkers/Draughts:



There are many games which use this or a similar board (this Wikipedia link lists some of them), but neither Qirkat nor any of the variants I know have a uniquely Lithuanian origin.

As far as I understand, this type of game board was rather wide-spread throughout medieval Europe, although exactly what games were played on them isn't so clear from country to country. Without, for example, pieces or instructions, both of which are generally harder to find in the archeological record, it's mostly a matter of speculation.