Lorgar is said to support Chaos undivided, does that mean he venerated all 4 gods as individuals or Chaos itself as a singular entity?
Also it has not been said how he was elevated to Daemonhood, he and Peturabo are not followers of any of the 4 Chaos gods, and no singular god would elevate a Daemon Prince without having them be aligned to them, considering the competition between the four Gods, that would make no sense.
You said Slaanesh different, how so ?
The emotions that powered Slaanesh have always existed, they just reached a point that allowed him/her to take consciousness from the melange of emotion that makes up chaos to my knowledge.
This is speculation, not saying it is fact, but I would imagine that since he has NO loyalty to the big 4 whatsoever, and no one knows exactly who elavated him to Daemonhood that he would be able to pretty much do what he wants.
He took leave of his legion before after his first Crisis of faith, now after his change of faith and it's vindication he took another leave.
I would like to imagine that he is up to something.
And please don't say BL would not allow it, I know that, part of the fun of the background is that we can speculate on what would happen, since the current timeline in WH40K is kinda static.
As far as faith goes, faith is faith undirected. When ultramarines slay orcs they empower Khorn, just by spilling blood and being proud of their martial ability. You do no have to say "Blood for the Blood God", just the very act of spilling blood gives Khorn power so to speak.
Every act of violence gives Khorne power, whether committed by his followers or by enemies
The Imperium gives Khorne ridiculous amounts of power, they don't do it willing to empower him, but that is just the way it is.
So faith, even directed at a Deity, or directed to faith in purity of duty, or faith in the truth of "the greater good" is still faith. And that should empower something in the warp.