The pulsating red staff was brought to Deckard Cain by Aidan during the Darkening of Tristram, retrieved from the depths of the Tristram Cathedral. This confirmed Cain's suspicions that Lazarus was responsible for the kidnapping of Albrecht. After Diablo's 'defeat', and the temporary respite afforded to the people of Tristram, Cain threw the staff onto a pyre. He noted that the fire seemed to 'embrace' the staff, and watched as it emitted green smoke as it burnt, emitting a high, hissing scream as it did so. Eventually the staff was completely incinerated.
The Staff of Lazarus is a quest item located on Level 15 of the Hell levels. When the player finds the Vile Stand, click on it. The staff will drop, and the player can pick it up. Bringing it to Cain triggers the Archbishop Lazarus quest.