When Bile Urchin dies, Mortuary and Ashes of the Abhorrent trigger.
Resolve the Mortuary trigger, putting Bile Urchin from your graveyard onto the top of your library.
Resolve the Ashes of the Abhorrent trigger, causing you to gain 1 life
Resolve the Bile Urchin ability.
Cast Bile Urchin from the top of your library by paying 1 life.
Repeat.
This clever loop turns the graveyard-hiding penalty of Ashes of the Abhorrent into a non-issue while using its lifegain trigger to entirely offset the cost of your engine. By sacrificing Bile Urchin to drain your opponent, you trigger Mortuary to neatly recycle the creature straight back to the top of your library. From there, Bolas's Citadel allows you to bypass mana costs entirely, letting you endlessly recast the rat for a mere 1 life each iteration while smoothly maintaining your life total through Ashes of the Abhorrent's steady healing.