For a better way to distinguish between the two pronunciations I think you're trying to get at, you can use /lunətɪk/ versus /lunætək/. The former is the only one I've personally ever heard and the one listed in most dictionaries, but I can believe that there are some dialects that use the other one. In case you can't read IPA, /ə/ is the unstressed neutral vowel (pronounced like the word "a" in quick speech) and never marks emphasized syllables, so if you don't emphasize the second syllable you're pronouncing it /lunətɪk/ and if you do you're pronouncing it /lunætək/.
Also, there is no difference in meaning between the two pronunciations - they're just different ways of saying the same word. "Lunatic" has only ever meant "insane" in English, sometimes with moon-related connotations, but never anything more. "Lunar" is the only proper adjective for moon-related things in English. In the case of the Lunatic Cultist, it's just a pun based on the word's etymology.