οὐδέ τις ἐστί
συνδαίτωρ μετάκοινος:

this clause merely delineates a situation, since ἐστί is in the indicative. While the first clause states that the immortals are not permitted to come near the Erinyes, the second states perhaps that they do not wish to partake in common. The two clause do seem to overlap.What construction do you believe ἀθανάτων δ᾽ ἀπέχειν χέρας to be?

If I understand the text, Gods belong to a different mode of being, there is no need to be 'commanded' not to interfere, they have nothing to do (ἀπέχειν) with the work of Erinyes, there is nothing common between these two modes, godly joy and bitter remorse.

Grammatically, I would connect ἀπέχειν with φαμὶ (as is κεκράνθαι), meaning that at the time when Erinyes are generated Gods have no participation (not that they "should not" have, but that they don't have, nor is there anything that correlates Gods and the Erinyes.

Fagles translates these lines thus: "Even at birth, I say, our rights were so ordained. The deathless gods must keep their hands far off, no god may share our cups, our solemn feasts." It seems like he is translating "phami" paranthetically.

Lattimore: " When we were born such lots were assigned for our keeping. So the immortals must hold hands off, nor is there one who shall sit at our feasting."

Somehow these two translators derived an imperative from these lines, and the only construction that I have found that correlates is the infinitive being used for the third person imperative.

If the Weir version of the text is accurate, what construction would these lines be in your opinion?
γιγνομέναισι λάχη τάδ᾽ ἐφ᾽ ἁμὶν ἐκράνθη:
ἀθανάτων δ᾽ ἀπέχειν χέρας

This is how Smyth describes the imperative usage of the infinitive:
"b. The infinitive for the third person of the imperative often occurs in legal language (laws, treaties, etc.), and does not necessarily depend on the principal verb. Thus, e)/th de\ ei)=nai ta\_j sponda\_j penth/konta and the treaty shall continue for fifty years T. 5.18 . In this construction the infinitive has the force of an infinitive dependent on e)/doce (it was voted that) or the like. So in medical language, as pi/_nein de\ u(/dwr it is well for the patient to drink water Hippocrates 1. 151." Doesn't it seem like there is an imperative from Fate in these lines?

If you do not agree with this construction what about this one Smyth mentions?
" §1304. The genitive with ei)mi/ may denote the person whose nature, duty, custom, etc., it is to do that set forth in an infinitive subject of the verb: peni/a_n fe/rein ou) panto/j, a)ll' a)ndro\j sofou= 'tis the sage, not every one, who can bear poverty Men. Sent. 463, dokei= dikai/ou tou=t' ei)=nai poli/_tou this seems to be the duty of a just citizen D. 8.72 , tw=n ni_kw/ntwn e)sti\ kai\ ta\ e(autw=n sw/|zein kai\ ta\ tw=n h(ttwme/nwn lamba/nein it is the custom of conquerors to keep what is their own and to take the possessions of the defeated X. A. 3.2.39 ."
Could this work?

Genitive of nature can not be our case, because it is not in Gods' nature to abstain from interference, on the contrary! Infinitive as imperative is normal, yet again it doesn't seem to fit here. Thus I would suggest Murray's text (same as Wilamovitz here). I would think of a translation like this: "when we are born such lots, I say, are assigned for us, and no immortal decides them, nor is there any of them sitting at our table"...

So you are saying that the lines in the form Smyth presents them are not translatable?