If I have a problem with this approach it is that it takes us out of Middle earth into a mythology of the primary world. I think there is another kind of mythological link being made here, & it is one that keeps us firmly within the secondary world.
In this episode I can't help thinking that Tolkien, having just mentioned
Turin, wants the reader to be reminded of the way he killed Glaurung - remember, he hoped to see the Silmarillion published - preferably alongside LotR. Both monsters are 'finished off' by being stabbed in in the belly from beneath by a mortal hero with an Elven blade. Even if Tolkien had the story of Lilith in the back of his mind we mustn't, or we'll be dragged out of Middle-earth into the realm of comparative mythology or worse
....