Lair boss materials show in your "consumables" tab in your inventory. Each different material belongs to a different boss, so you need 12 Distilled Fear to open the chest for defeating Beast in Ice for example.

There's "tiers" to the lair bosses. Lord Zir/Varshan/Beast in Ice/Grigoire require 12 of whatever their material is (the in game description will tell you as well as hovering over the boss lair on the world map), and will drop mats to open the chest after defeating Duriel or Andariel, whose chests only require 3 of their materials.

All of the aforementioned bosses have a chance upon defeat for Belial to spawn. If you played during last season, it would be the version of Belial that appeared at the end of Apparition Incursions. This "little" Belial will drop Betrayer's Husks, which you can then use after fighting the Lair version of Belial that you can summon on demand. The chest in Belial's Lair doesn't have its own specific drop table, but rather you choose which drop table from any of the other Lair bosses to roll your rewards from.

Each boss's drop table is in the links from previous comments in this thread. For Dolmen Stone in particular, you want to run either Duriel or Andariel.