"whether the pious or holy is beloved by the gods because it is holy, or holy because it is beloved of the gods."
If the first, then the gods are subordinate to whatever is pious or holy and then wouldn't be gods; that which is pious or holy would be more divine than the divine.
If the second, then what is pious or holy would be utterly arbitrary, subordinated to the implacable and changing will of the inscrutable gods.
This poses a particular conundrum to the Christian world that holds the tenant of an omniscient, omnipotent god. The solution of this fellow seems pretty good:
Indeed, goodness and holiness are what they are b/c they are united with the goodness and holiness of god. The god is good and holy such that all goodness and holiness are mere reflections of his character.
What most people miss, it seems, is that this dilemma and the solution Plato wishes us to see through the dilemma is itself an example of the indefinite dyad.
The indefinite dyad was a source of wonderment to Plato who holds it to be the basis for everything that exists. Plato held that the indefinite dyad could be seen in everything in the created world - it was a map upon which all creation rested and was, indeed, the blueprint of the divine itself.
The indefinite dyad was a proportion between three things wherein the first thing was to the second thing as the second thing was to the whole. This was represented by a line cut unequally in two parts such that the lesser cut (line a) is to the greater cut (line b) as the greater cut (line b) is to the whole (line c); or put mathematically a:b::b:c. This is the same divided line and "lesser and greater" which he speaks of in "Republic". The indefinite nature of this twofold cut, or dyad, was a proportion, not a specific number though it was, in the golden division, directly related to the number represented by PHI. Plato, like other followers of Pythagoras, contended that all existence emanated in its multifarious forms (what he refers to as "multiplicy") from unity, or "the monad". Monad cut into dyad is divided again and again to produce multiplicity. But the relation between the multiple things existing in creation and the unified monad from which they sprung was one of unity. The lesser and greater multifarious forms were intimately united to the reality of the monad from which they sprung.
In Euthyphro the lesser (in relation to the gods) would be gods subordinated to the good and the holy; the greater (in relation to the gods) would be complete and arbitrary control by the gods over what was good and what was holy. The indefinite dyad, however, was always a dilemma set for students to be able to comprehend the whole, or as Aristotle called it, the "middle way".
The Euthyphro dilemma, therefore, should lead us not to accept the greater or the lesser, nor to throw out Plato's writing as offering no third solution, but rather, by wrestling with the dilemma, come to a deeper understanding of what the relation of the many (lesser & greater) might be to the one.