The "Red Alicorn" is the moniker given to the false Alicorn living under the Steam Plant outside of Bittsburgh. It was presumably one of the twelve unicorns who cannibalized Princess Luna's power during the Third Era and ascended to Alicorn-hood, along with Astrallania and Prince Solstice.
Sleeves, Lozenge, and Double Down covered its stasis tube in explosives set to go off the moment it moved. It then awoke, triggering a massive blast that destroyed it. The inadvertent avalanche triggered by this event becomes a major plot point in the second and third "books" or "gospels" of the original novel.
Lozenge remains conflicted about their actions. She states that they didn't know anything about the alicorn, and killed him not because of how he behaved but because of what he was.