Balor has been a thing far longer than D&D or Lord of the Rings. While D&D's Balor is based on the Balrog, the original Balor is an Irish myth, the king of the Fomorians noted for his powerful flaming eye covered by seven eyelids and if all were opened the entire area around would be utterly destroyed.
Given this Balor's power set, it's obvious that he's based on the mythological Balor rather than the copyright/trademark dodging D&D Balor.