Don't purchase checked luggage with the OTA . More expensive and you don't know if the data is transferred correctly to the airline or if the airline will honor it.
Sorry I don't have any experience with luggage fees with LOT or LH. Did you check the webpages of LOT and LH for information? It is cheaper to buy in advance on the webpage of the airline than at the airport on the day of traveling.
Did you check the fares to TYO which include checked lugage? Most likely cheaper than adding 1-2 checked bags.
Maybe it is cheaper to send or ship the luggage in advance with courier or the like ? At least for the return flight to Poland it should work OK.