@imnotcreative
I can speak from experience on this one (as anecdotal as it might be): my undergraduate education was not regionally accredited (just nationally, ABHE), however, I was able to perform exceptionally and got admitted into "top-tier" graduate programs, and subsequently admitted into a few "top tier" PhD programs. This is of course not standard scenario, but I would suggest that Liberty, while seemingly unhelpful, is not detrimental to your chances of furthering your graduate education.
My advice is as above: 1) do your undergraduate program and do it well, 2) take things like the GRE seriously, 3) network with your professors (they presumably came from programs you might be considering yourself), 4) contact the universities you are considering for your graduate degree and ask them questions about their relationship with universities like Liberty and 5) take your academic interests seriously (attend conferences, write proposals for conferences, etc). There is no way to emphasize #3 and #5 enough; if you are just one application among the hundreds to your program, you are generally less likely to stand out--even with an exception GPA and GRE score (see https://www.insidehighered.com/news/2016/01/06/new-book-reveals-how-elite-phd-admissions-committees-review-candidates). Meaning, be a face to the programs and people you want to be with, but even more so, be someone they can begin to see as a junior scholar and as someone they can mentor.
I hope some of this helps.