I don't know much about Lyman D. Hudson, but found the photo above among the family photos that my Father had at the time of his death.  I don't have Lyman listed as a brother of my father or his sister but it is signed "Your brother". 

Research Notes

One researcher mentioned that the photo appears to have been taken earlier than 1896.  It was taken in Indianapolis, Indiana, by L. D. Judkin's Art Chambers.  I noticed several references to a Lyman O. Hudson in the Clark County, Wisconsin web pages.   I also discovered a Lyman O. Hudson marriage to Hattie F. Scott 10 June 1873 in Fillmore, MN.  I've found a Lyman O. Hudson born 30 Jan 1853 in PA.  He died 29 Dec 1933 in Colby, MN.  Father George Babcock Hudson b 13 Dec 1822 in Scipio, Cayuga Cty, NM...mother Pamelia Ann Whitfield born 10 April 1827 in NY.  This Lyman married a Nellie M. Miller born 5 May 1873 on 7 Dec 1897.  Also found a Lyman O. Hudson who married a Lizzie Dunn 24 Oct 1864 in Marion Cty, Ind.  I am hoping someone might recognize this photo and help me break through this brick wall.  Lora Hudson Treadwell