One of the big questions to figure out if this is a classic “alternate timeline” where the Horus Hersey never happened or if it is happening concurrently with the existing WH40K someplace else – or if it somehow takes place within the canon WH40K universe but in a different time. This is actually possible because the Immaterium does do funny things with time and if we are postulating some of lost colony this is a somewhat viable idea.
Location in place is a bit more problematic for a couple of reasons. As written the setting of WH40K basically covers the entirety of the Milky Way Galaxy. So the idea that there is another large, “uncontaminated” human empire is somewhat of a no-go – so that leaves open the idea of placing the “Lost Imperium” in another galaxy and there is an interesting question as to if the Immaterium would actually exist in another galaxy given that it is the Sea of Souls.
Plus, we want to have a universe with as many of the familiar tropes as possible. I want a universe with some version of Eldar for example – though I don’t exactly care about the Tau or the Orks or some of the other races unless there was a really good reason. but if we place this in another galaxy we also have to come up with an explanation of why and how they are there also.
But, it could argued that at some point during the War in Heaven with the C’tan the Old Ones created a “back door” or some sort of escape route to another galaxy. This is also somewhat reasonable, and could explain why there are some very similar races. Also, the existence of the Tyranids proves that there is extra-galactic life out there – and they don’t seem to be soulless in the same manner as Necrons and this suggestive of an Immaterium elsewhere.
But that seems like a decent idea. Somehow, during the Great Crusade some large group of humans tripped over a Old One escape hatch left over from the War in Heaven and ended up in another galaxy – and perhaps one that was also seeded to some degree by the Old Ones with some of the proto-Eldar and perhaps other races that they created. The timeline is concurrent with the canon setting, but in some other galaxy far removed from the Terra.