League of Shadows Lair

The lair of the League of Shadows was a large stone and wooden temple construction on top of a snowy mountain in an unspecified Asian country. It featured a throne room for Ra's al Ghul, at least one elevatable prisoner cage, and an assortment of ninja weapons.

Destruction
The lair was destroyed when Bruce Wayne decided not to be a part of the league's plans. Upon being ordered to execute a prisoner, he used his sword to flick an ember onto some explosives, creating a chain reaction that destroyed the entire building.

Either enough personnel escaped or there were auxiliary bases as the League of Shadows regrouped and attacked Gotham city afterwards.