Does Lighting Shriekers ability activate if it dies or was exiled?
There's no conditional on that effect, except "At the beginning of the end step".

Roughly speaking, any effect is going to apply only when the card is in play, "on the battlefield", unless the effect specifies otherwise.

So the effect takes place when it says it does, roughly at the end of the current turn.  Not when it dies or is exiled.  Since the card has Haste, in effect, you get a 5/5 attacker with flying &amp; trample for one turn only that then gets shuffled back into your deck.  Unless you have some other way to tinker with the mechanics, that effect will always take place at the end of any turn.

To clarify further, your tumblr information is correct; if it dies, and is in the graveyard at end of turn, the effect will not apply, and it will stay in the graveyard.

Something that can exile the card and then bring it back the next turn would, temporarily, circumvent the effect, if you want to keep it in play. (I thought there was a Blink card that would do this, but cannot find it now).