Iuz as a 5e Demigod can fit into the definitions of 5e demigods, but it is some work.
5e Demigods can ascend and become full gods. If you consider Grazz't a god in 5e then Iuz is a demigod under the Quasi-deity sidebar definition and he can ascend to full god status who grants spells to clerics. In GH lore that is my understanding of what Iuz did, coming into older edition demigod deity power with his own clerics.
In 5e this would put him as an ascended Lesser God Demigod, similar to Greek Heracles and Dionysus, while most 5e demigods are mortal bigger than life heroic people like Theseus and Perseus and are classified as quasi-deities who do not hear prayers.
Zagyg however would require additions to his story to be called a 5e demigod as there is no indication that he comes from divine parents, he just did a big magic ritual to ascend to become a god.
Grazz't brings us back to the demons and evil gods split.
5e in the DMG makes the distinction of gods who grant cleric spells and non-gods (quasi-deities) who do not.
The 5e MM is not entirely clear on the status of things like demon lords. Page 51: "The chaotic power of the Abyss rewards demons of particular ruthlessness and ingenuity with a dark blessing, transforming them into unique fiends whose power can rival the gods." The phrasing can rival the gods implies they are not gods themselves, but does not say so explicitly.
Lolth in the 5e MM is described as a goddess who became a demon lord. It does not specify whether she is no longer a goddess or whether she grants spells to clerics, but it does call her the matron of drow and refers to her priestesses, her faithful, and her followers.
The 5e DMG page 12 mentions fiends as non-deity lesser spirits who might grant spells under a certain number of "if" conditions.
"If you introduce a monotheistic religion into your campaign, you need to decide whether other gods exist. Even if they don't, other religions can exist side by side with the monotheistic religion. If these religions have clerics with spellcasting ability, their spells might be powered by the one true deity, by lesser spirits who aren't deities (possibly including powerful aberrations, celestials, fey, fiends, or elementals), or simply by their faith."
This seems like the DMG laying down options and not establishing a D&D baseline. Alternatively this could be read as consistent with a baseline that all lesser spirits can grant cleric spells in D&D or that only under these specified conditions can non-deity lesser spirits grant cleric spells and go against the baseline that such non-deities cannot grant clerics spells.
5e seems ambiguous on the status of fiend lords.