Carol, I see that you have tested, and that you've been wondering about this question for some time. Nellie and Lillie were sisters, is that right?
If you have strong DNA connections to their family, the theory that Nellie could be your biological grandmother seems to make sense. I assume Nellie had no children of her own? Are there any surviving family members (or their descendants) that could give you any information? Did Lillie have children of her own, whose descendants could be tested? Did she and Nellie have other siblings?
(P.S. Unless you've taken an mtDNA test, I'd remove the mitochondrial tag.)