It's really hard to predict since she isn't objectively GREAT and critics' opinions on her are way too varied.I personally loved her album,voice and especially the writing-style,but can't say if Grammy Committee will have a positive opinion on her.I feel like she might not get any.But there could be a surprise.
Grammys reward commercial success in the US, critical acclaim, and then they add some random unknown nods to maintain their credibility. Lana doesn't fit in any of those categories.
None, after the critics decided to rip her a new one I doubt the grammys will treat her any differently.
Anyway Grammys don't make or break careers, fans who cling on to their fave's grammy records do it for the validation they desperately crave for their idol.