This is because she started out as a sort of stock character: the kindly old lady across the way who gives out cookies and treats despite what Mommy might have to say about the matter. This being sort of a foil to Elly might have persisted for some time were it not for the sort of need Lynn has to explain to the world that old married couples usually downsize when one of them is too poorly to function well and that old widowed ladies move to the nursing home because they don't want to die in their real houses. It was then that we found out that her husband died fairly young and it sort of broke her because she didn't want to betray him by moving on with her life until it was pretty much over with anyway.
While she did tell Elly not to take John for granted because it could end just like that, what really captured Elly's attention was having to help her sort through her belongings to see which of her nieces and nephews got what because she had a sort of wake-up call. After all, she felt that she was nearing senility herself at that point and seemed to have been under the impression that Lizzie would be spending the day after her senior prom divvying up her poor dead mother's belongings with Mike. Most of the gloomy commentary about why no one seemed to have done too much to help the poor old woman while she was alive to appreciate seem thus to have been rather self-serving as she saw herself in her old neighbor and cast herself as the neglected old lady being asked to die quietly in the corner so as to not disturb people.