I agree. I think other religions would be able to use Lifegiving, through other 'channels.' Eissa's power is part of the Lords of Orhan doctrine.
Would this then mean that worshippers of gods outside of the Orhan pantheon do not pass through the Gates of Oblivion when they die, and instead go elsewhere?
Or is it that Eissa allows the other gods (Charon, local, or otherwise) to bring back souls over which she has no "dominion"?
The "where do souls go" question can usually be left vague, but given the number of times the typical adventuring party will want to obtain a lifegiving spell, it bears some thought and consistency.
I'm thinking that at least for my game, I may use the Gate of Oblivion as the nexus for souls claimed by the gods of Orhan, with other gods having other destinations or uses for souls. This would seem to be supported by the big crystal consuming the souls of Zanar worshippers as described in the Powers of Light and Dark.
And for non-worshippers, there is either the Void, or nothingness. Kind of makes being an observant adherent of some kind of religion a bigger selling point.
At least if you want to ever be brought back from death.