I think scrapping everything you have created so far and swapping over to a new library that requires learning and experience of the api all over again and yet does not serve any extra purpose required of it over the original would not lead to less worries. Quite the opposite.
In fact we have pointed @wessles to a library that is standard in Android, requires no specialised setup and shares 100% of the core features and api to what he is used to. I have no interest in starting a grudge match between LWJGL and LibGDX - people can use whichever library they want to. But I do think you should extrapolate that thought out into not badmouthing other libraries purely because they are not your own choice.
If this was directed at me, then I do not know what You mean by "badmouthing". I did no such thing. As the op was asking a question of "does it work", with libgdx, there is no such question, because it sure does work, hence the reference of "use libgdx and have less worries".
Also as the OP did not specify how much code there is already in place, the point about "scrapping and swapping" is moot. In case multi-platform support is desirable then the time spent to learn the library is well spent.
I myself have rewritten my game from java2D -> slick -> libgdx, as such I am well aware of the effort needed and I do not regret doing it.
The question boils down to if the OP wants to make something workable, a product, in which case productivity is the key and libgdx offers more than lwjgl. In case the OP wants to tinker and write stuff, experiment, learn etc., then the question presented in by the OP has less weight since even if lwjgl doesn't work on andriod, the OP could just make it work (or learn that it's unfeasible) as a learning exercise as a sort.
I do not see any bad-mouthing lwjgl nor even any negative attitude by me towards the library.
If it wasn't directed at me, well then... sorry and carry on.
Edit: Also, not really comparing and am well aware of the differences. I was just suggesting something that in my mind might suit better.