"On the GM putting the LoC on an advantageous footing, of course he would. It's not arbitrary, it's treating the LoC how he should be. He's a genius, described as a criminal mastermind and a master of plots -in fact, they are created from lies, conspiracies, and plots, it's all they are. If the GM just left him standing in the middle of a cave waiting for a psyker to come along for a proper showdown, then the GM missed the bus completely on what those things are all about. Not placing them in an advantageous position would be a grave injustice to what they are. Just read up on the one presented in ascension. He would play very dirty indeed.
And the psyker, even in the unrealistic showdown situation, wouldn't necessarily go first. The LoC has Preternatural Awareness as well. Anything the psyker can do, he can do as well (and more). Granted, the psyker gets a higher bonus to add, but the LoC could be running about with a bit more overbleed -you can be guaranteed that he pushed with full dice as he don't care about phenomena (9's are is friend and increase his overbleed after all ;-) ). Still, it's a bit of a pointless exercise as the original math was done in a complete vacuum and you would never meet an LoC under such conditions unless the GM as completely fallen asleep. In the end, all those numbers really don't mean much in the game proper.
I seem to recall this exact discussion about Holocaust... (and psykers in general... but that seems to have worked it self out when things stopped being hypothetical and began actually being real in-game accounts of what happens when the psyker isn't in an ideal vacuum any longer...). Granted, they're still hell on wheels, but they don't seem to be as atrocious as some of the earlier vacuum damage numbers were making them out to be. Noting happens in a vacuum (and not that space vacuum, wise-ass ;-p ), not all stats will be optimal, perfect, or close to it, things don't hang around waiting for you to get the on them, tings can fight back, etc. And I think if I say anything more, all I'd be doing is repeating what I've already said."
It is arbitrary if the GM effectively makes it so that no matter what, the LoC is always going to be able to get the on you; that's not an appropriate way to mitigate the Psyker's power. If the Psyker makes a mistake, or acts predictably, etc, fine, by all means, give the LoC his surprise attack, but otherwise, it's silly and unfair to just arbitrarily rule against the former.
Also, no, the LoC cannot consistently achieve the same level of Initiative a mid-high Primaris or Inquisitor Psyker can. Psykers get a substantially higher WP bonus and more Psy Dice, which makes for an exponentially higher result, particularly with Invocation involved:
55 (5.5 * Psy Rating 10) + 54 (WP Bonus 3x, * Invocation) + 4 (Discipline Focus + Power Well 2) + 5 (Discipline Mastery) = (118 - 9) / 10= 10.9 = 10 * 27 + 27 = 297 bonus to Initiative.
LoC = 66 + 32 (WP Bonus 2x * Invocation) + 5 (Discipline Mastery) = (103 - 9) / 10 = 9.6 = 9 * 16 + 16 = 166. On average, the LoC will incur 1 Psychic Phenomena, so we increase this to 182.
The difference? A 'mere' 115 points of Initiative.