To be honest, there isn't much lore so much as a general theme. I originally came up with the idea back when I actually played 40k in the days of 5th edition. Even then I wanted Necrons painted up to look like they were carved from obsidian and based in something that didn't look like dead, barren wastes. So I came up with glossy black Necrons based in swamp bases I got from Secret Weapon Miniatures. That army I since sold off when I fell out of the game shortly after 6th ed came out. When Indomitus came out I fell in love with how the Necron models looked and decided to get it. This time I went about creating the paint scheme in a different way.
Using a bright red undercoat, I made a really nice obsidian looking scheme by covering that in a layer or two of Minitaire's "Oil Discharge" Ghost Tint paint. For the bases, I took inspiration from the Vex machine worlds in the game Destiny like Nessus, as well as Urdak in DOOM Eternal. Alien colored grass, plants, trees, and soil.
The Khor'akth Dynasty resides in the galactic west, in the Segmentum Pacificus. The royal family was known for their exquisite gardens and after awakening from the great sleep, turned to terraform the planet back into it's former glory after decaying into a fetid swamp. In the process, they had also exiled all those who fell to the Destroyer's curse to what would be, imaginatively named, the Destroyer's Moon to keep them from constantly trying to torch the gardens.
They are in possession of a C'Tan shard, a shard of a minor C'Tan known as the Lady of Sorrows. I was in fact going to use a converted Lady Olynder model for this, but found something better to 3D print and use.
Other than that I haven't really expanded upon this, I just wanted a unique-ish theme for the models in my curio. If I think of anything else I'll be sure to add it.