The two words have nothing to do with each other, in the end. You could have guessed that, maybe, but you know for sure when the etymology identifies the verb loom as being Scandinavian in origin and perhaps being related to the word lame. The noun loom, meanwhile, comes from Old English and would seem to be related this Old English word andloman, meaning “apparatus” or “furniture.”
But then there’s the penis.
The second sentence of the entry for the noun loom throws a curveball. I quote: “Originally ‘implement or tool of any kind’ (cf. heirloom); thus, ‘the penis’ (c.1400-1600).”
No explanation of that. Just “thus, ‘the penis.’”
See? And you thought looms were boring.
In closing, I would like to say that no discussion of looms — penile or otherwise — would ever be complete without this throwaway joke from The Simpsons.