Cast Acererak either from your hand or from the command zone by paying plus commander tax, if applicable.
Demon's Horn triggers, causing you to gain life.
When Acererak enters, its first ability and Carnival of Souls trigger.
Resolve the Carnival of Souls trigger, causing you to add and lose 1 life.
Resolve the Acererak trigger, returning it from the battlefield to your hand, and venturing into Lost Mine of Phandelver.
Repeat.
This loop is a masterclass in recycling triggers, turning Acererak the Archlich's self-bouncing entry into an engine of endless value. Normally, casting the lich for three mana would be a slow trek, but Planar Gate steps in to discount his cost down to a single black mana, perfectly offsetting the mana generated by Carnival of Souls each time a creature enters. To keep you from bleeding out while fueling this dark ritual, Demon's Horn steps in to offset the life lost from the carnival, turning every loop into a net-neutral or positive exchange of resources. By repeatedly casting and returning the lich, you endlessly venture into the dungeon to bury your opponents under an avalanche of tokens, resources, and triggers.