Both "livestream" and "live stream" are correct, but they are used in different contexts. "Livestream" is a compound word that refers to the act of streaming live content online, while "live stream" is a noun phrase that describes the actual live content being streamed. In regular streaming, the media content is processed and presented steadily without losing its continuity, whereas, in live streaming, it’s recorded and transmitted simultaneously in real-time. ^{textranch.com 1 2}