NOTE: Lucille BROOKSHER's pneumonia probably started off as the flu, since this is reported in the midst of the infamous 1918 "Spanish flu" epidemic, and many other articles from this newspaper issue report people sick with the flu.
A quick search over at Ancestry.com gave me a William R. BROOKSHER
1920 United States Federal Census,
living in Fort Smith, Arkansas. A 20-year-old daughter named Lucille lives with the BROOKSHERs, so it appears that she made it through the pneumonia, if this is the same family.