Well, besides Bêthberry's answer, I think there's nothing as unusual on Lúthien's ability to shapeshift. I am pretty sure Melian could have shapeshifted, we are told that she took the form of one of the Children of Ilúvatar just because of Thingol (I could put a quote in here but I am too lazy now to look for it, sorry
). Also, she was a Maia, and they were all able to pick the shape according to their choice, at least in the beginning, so some part of this ability could have been given to Lúthien. (By the way that does not mean that Lúthien would've gained every ability her Maia mother had, just some of them, and probably with lesser power.)
As for killing Morgoth... I highly doubt Beren and Lúthien would have been up to the task. Even getting one Silmaril was enough, and if anything happened, the whole Angband host was upon them. Not including Morgoth himself. And Lúthien wouldn't risk Beren's life even if she had the chance to use some Elven or higher power to escape. Not that anyone could escape Morgoth when he was awake. Not that anyone could even kill him even if he was asleep, after all, he was a Vala. I think you'd find the best answer to this question if you asked Fingolfin. And, not to forget the last thing, stabbing someone in his sleep just is not a thing a person does in Middle-Earth. That's reserved only for the wicked evil creatures, like the Nazgul, Orcs and similar. It won't be fair, I am sure (not to mention that such a deed would bring reluctance among the storytellers and bards of Middle-Earth, they'd be surely strongly confused whether to even make a heroic song of it. That'd be the biggest crisis in Middle-Earth. So no, that wouldn't be possible).