Greek sources do not agree on where the Fates stand in relation to the gods, and the disagreement is not a gap waiting to be filled. Hesiod names them twice with two parentages. In one passage of the Theogony they are daughters of Night, alongside Doom, Blame and Retribution; in another they are daughters of Zeus and Themis, sisters of the Seasons, and Zeus gives them their honour. Antiquity did not reconcile the two, and both readings stayed available: fate as older than the gods and outside them, or fate as an ordinance of the ruling god.
The Iliad puts the question at its sharpest. Zeus watches his son Sarpedon go to his death and considers lifting him out of the battle, and Hera answers that he may do as he likes but that the other gods will not approve of a man long due to fate being released from it. Zeus weeps tears of blood and lets him die. The passage neither says that Zeus could not have saved him nor allows him to do it.
Plato gives them their most elaborate setting. In the myth of Er at the close of the Republic the three sit on thrones around the spindle of Necessity, singing of what was, what is and what will be, and turning the whorls of the cosmos, while souls choose their next lives before Lachesis. The choice is the soul's own, and it is then ratified and made irreversible, which is a considerable philosophical adjustment to the older picture of a thread cut by somebody else.