The Lord God is one, not three.
What you refer to as the "Lord God" is merely a megalomaniacal typal being (with anthropopathic traits) of a particular plane that could be the cosmic vital or at the most one of the cosmic mind planes.
The typal beings of any plane can manifest in multiple forms in their own domain as well as on the planes that're inferior to their place of origin just as H2O can assume three aspects (solid, liquid and vapor) in the physical sense.
So, the Christian Trinity of father, son and holy ghost means this - father is the manifest form of the archetypal being of a particular plane, son is the physical embodiment of the father, holy ghost is the innate causal mechanism that causes the father to embody itself as the son. Each aspect supports the other and is causally related to the other and logically speaking the triune aspects are simply seen as the multiple functional modes of a single typal being of a particular plane. There's no mystery regarding the trinity. Biunes, triunes, quadrunes, pentunes and so on are common features of nature and being and constitute the multiple manifestations of a typal state of existence.
Mind, vital and matter with their numerous sub-planes constitute the triple lower planes in the Manifestation.
The superior planes commence from the cosmic overmind which encompasses the 9th, 10th, 11th and 12th planes of the cosmic gradation.
The supramental planes and those planes that exceed the supramental begin from the 13th cosmic plane.
Each plane has a different poise in terms of degree of consciousness and the concomitant energy.
Differences in the Manifestation are due to degree of manifestation and are not of kind since oneness underlies the totality - a unified field of consciousness-energy manifests as a gradation.
Reality can only be expressed in terms of consciousness and energy and their gradations.
Everything else is fiction.