How do I get the chest outside Mitula’s Sanctuary – the one on the island in the lake around the temple?

The answer is really quite simple: you can’t get it in the USA or European versions of the game. In the original Shining Force game, characters could search during battles, but in the USA and European versions of Shining Force 2, they can’t. The option is available in the Japanese version of the game (when the game was translated, a few features had to be removed so that it could fit on the cartridge), and this chest contains a Shining Ball.

The unreachable chest at Mitula's Shrine in Shining Force II