I'm assuming you are strictly talking about the Western Left Hand Path (as opposed to the controversial 'Eastern' LHP)?
I would have to say that whether you are theistic or non-theistic, it depends on your definition of the WLHP.
My personal definition is: cultivating and nurturing one's Isolate Consciousness as a separate and unique quality separate from the Objective Universe and its variations through various degrees of Antinomianism.
So, if the Satanic, Setian or Luciferian theist is indeed pursuing that goal, then I would qualify them as Western Left Hand Path.
That seems to me rather restricted to one cosmology. I don't think such a restriction fits the LHP well - but for a personal definition it probably works fine.
I for one might be considered a RHP satanist by some of the definitions in this thread, but I nevertheless consider myself LHP.
I don't believe in the existence of a truely objective reality - it's all just (in) the mind of the divine, and we, as parts of it, always see only parts of that mind, from one perspective. So there is nothing we could separate ourselves from. Even the desire to influence reality and to separate oneself is nothing but an aspect of existence.
However, I still aim for self-deification and intend to use heterox or antinomian practices for it if I can and if it helps me. This is my goal since even though ultimately all just is I have the impression that at least the part of all in which I am now (e.g. the cosmos or just merely my own body-mind-complex) could be in a more comfortable shape than it is, and might not need to remain bound to the ignorance and causal restriction to which it currently is.
Furthermore, I venerate a deity whom I submit myself to and of whom I consider myself to be merely a manifestation. Or, in other words, I believe myself to be divine in essence and my inner will to be the god of my world. Am I LHP now or RHP?