There are a number of Cthulhu Mythos cults this cult could be based on.
The Cult of Cthulhu chant the prayer ph'nglui mglw'nafh Cthulhu R'lyeh wgah'nagl fhtagn read from the Necronomicon to begin their meetings. The prayer translated means, "In his house at R'lyeh dead Cthulhu waits dreaming".
When Coon and Friends were selling lemon bars to help with the damage Cthulhu was causing in the Gulf of Mexico, the cult leader bought the last of their lemon bars, and taunts them by saying, "There is no way for them to stop the almighty Cthulhu".
Mysterion learns of his parents involvement with the cult ten years ago while investigating the cult with the Coon and Friends on the internet. While spying on the cult they notice another cryptic chant, "That is not dead which can eternal lie, And with strange aeons even death may die".
Thinking the cult has something to do with his super powers of regeneration, he does his own detective work to find out about his origins. Mysterion asks the Goth Kids what this phrase means but is murdered by the cult leader in an ambush.
In "Coon vs. Coon & Friends", Kenny is reborn by Carol McCormick, she expressed regret for attending the cult meetings in the past, hinting that Kenny's frequent deaths and resurrections may be related to the cult.