The Lyceum is located inside Blackrock Depths, and is accessible from the Summoners' Tomb. It leads to the Iron Hall past a magically sealed door. A lyceum is a place of learning, so this is presumably where the dark irons come to hear speeches or lectures from the senators and their emperor.
This room is filled with vast numbers of non-elite, low hp dwarves, linked in groups of 10 or so. These dwarves are on a fast respawn cycle, with a number of patrols wandering through the area. On the far side, the doors to the Iron Hall stand locked and unpickable. Two braziers flank the doors, each guarded by a fire elemental. Two flamekeepers are within the room at any one time, with about 8 possible spawn points spread around the room.
To enter the Iron hall, you must loot two torches from two Shadowforge Flame Keeper (one torch per dwarf), and use it to light the two braziers. These are five minute duration, unique, BoP items, that are consumed on use. Once both braziers are lit, the doors open, and the NPCs of the Lyceum stop respawning.
The key to this room is to stay together and keep moving, to avoid undue aggro and the (approx) 30 second respawns. Even low level aoe is very useful here, such as a paladin's consecration. Have loot set to free for all, to make torch looting easier.
Some parties will send a single rogue or druid to kill each flamekeeper and loot the torches, while the rest of the group works their way to the braziers. This is risky because if the stealth class aggroes extra mobs, they will often die, leaving four players to do the work of five. The risk is not worth the lack of reward.
A better tactic is for the party to stay together, staying to the right wall, until they reach the right brazier on the other side of the room. Rogues are useful here: be on the lookout for the patrols, ready to distract them. There is a safe area on the braziers' platform where approximately lvl 55+ players are safe from the constant respawns and patrols, where the party can rest. From here they work around to the left brazier, where there is a similar safe spot. You may also want to make a macro with /target Shadowforge Flame Keeper to help find the flame keepers.
At this point you will have covered nearly half the spawns of the flamekeepers, and will have otherwise located them.