Somewhere at hell level 15, find Lazarus' Staff. You will have no idea of what to do with it. So, backtrack to Tristram and talk with Cain. He will tell you about Lazarus' betrayal and his plan of making a ritual with Prince Albretch so he could be the vessel of Diablo himself. Cain has hopes that maybe Albretch is still alive and will ask you to hurry up.
Fill your inventory with potions and things you may use, as this boss is pretty hard to kill. Backtrack to level 15, and close to a huge pentagram there will be a red portal that will lead you to Lazarus' Lair. Enter it.
The room will lead you to Lazarus anyway. However, it's pretty messed up. There will be rooms that holds a teleport pad that will teleport you to another room on this level, which is filled with monsters. There are also two books here.
Go teleporting your way until you reach the last room, where Lazarus is. Be careful when teleporting, as the room will always contains demons. This level only holds advocates and Succubus witches that attack with magic.
Lazarus is much like an advocate, his attacks will always be magical. When you reach him, beware, he will come with an huge horde of demons and two unique demons as well.
Killing Lazarus with melee weapons is quite difficult, since he will use Flash spell on you and will keep teleporting far away from you. Ranged weapons are useful and Stone Curse is a good strategy to kill him. With Stone Curse, keep cursing him and attacking until he dies. Alternatively, try to corner him. To properly use his teleport, Lazarus must have a valid path of movement, clear of any obstacles (walls, candle lights etc.) Remember those book stands you used to teleport to Succubi? Try to corner him between such bookstand and the wall. Easy picking.
After killing him, you'll discover that the boy used on the ritual was not Albretch. Backtrack to Cain to finish the quest and start the final one.