I really don't have any information for Lidia "Liddy" (LUTMAN) WILSON, other than the census after her marriage.
Don't you think that she is the daughter of Samuel and Catherine, but instead of being born March 1879, as the 1900 census says she was, that she was actually born in March of 1881, and the reason that she does not show up in the LUTMAN household in the 1880 census? And, her not showing up in the LUTMAN household in 1880 is why researchers don't include her in their data?
Samuel and Catherine had a daughter, Fanny M. LUTMAN, born September 1878, and I do not know what became of her.
Also, Alice Flora LUTMAN, who married Seth RUTLEDGE, 1890, in Monroe Co., IL., is another one that I do not know how or if she is related to Samuel and Catherine.
Sorry I can't be of help with Lidia. If I find anything about her, I will send it.