One of the interesting things about positing the Lost Imperium in another galaxy is thinking about what “the Warp” would be like. Arguably there would be no, or at least very different, Ruinous Powers – and there is certainly no Maelstrom or Eye of Terror – and might have more in common with the Formless Wastes than the Realms of the four Chaos Gods.
In general I think that making the Immaterium of the Lost Imperium’s galaxy an essentially calmer environment than that Milky Way would be interesting. We are already positing a setting far more grounded in the Imperial Truth than the Imperial Creed which also suggests a less chaotic universe less dominated by the powers of Chaos. This may be because the native races have never spawned quite the level of psychic energy to birth Chaos Powers the same way as in the Milky Way, or perhaps they have successfully combatted them – that’s almost too much to speculate at the moment without figuring out what the dominant races are…
So let’s do that!
We’ve already suggested that this galaxy was seeded by proto-Eldar (which we’ll call Eldar) by the Old Ones. Personally I’m not a fan of the Orks in WH40K but perhaps there is an analog of them as well – but if we agree to that I am going to make them far, far less “Ork-y”. I’m more tempted to simply say that there is something more like the Tyranids or the Kroot that act as the Old One “spore race.”
More so than that, if we are positing a new galaxy, I’m even more tempted to simply invent a new major power that is inspired by both the Necrons of WH40K and the universe of Stargate: Atlantis – the Raith. Perhaps the reason the Immaterium is so calm is a combination of a non-corrupt, non-dying Eldar race that has managed to successfully not “irritate” the Immaterium plus a soulless race that has been harvesting the souled races for “food” in periodic harvesting runs and also managed to keep the “psychic noise” down and thus prevented the same sort of rise of incredibly strong or dominant Chaos Powers. Alternately what we could posit is Malal as the “dominant” Chaos Power over a pantheon of lesser Daemon Princes and various creatures of the Immaterium – again, another discussion.
But in any case, all of this also starts to point the way as to why there is not any need for the Astronomican or why it exists in a significantly different format. If we are trying for an analog of the Imperium then we should have some sort of Astronomican but it can’t be the same thing (simply being impossible to duplicate technologically). I also don’t want to go so far as saying that there is an Imperial Webway – which is a reasonable extrapolation of the Great Crusade era – because we haven’t decided if there is a Webway used in this galaxy by the Eldar (though it would be hard to imagine an Eldar race without it).
But, in any case, this leaves lots of room to develop and expand upon the overall setting.