Lavina Bates, age 24 in 1880, could be Arley Oscar Bates mother. If she is the daughter of the 85 year old and the 66 year old, her maiden name would be the same as theirs, however, she could be using the Bates surname from her husband. Here's Levina Terrel in 1870->
United States Census, 1870
||Indiana, United States|
|Birth Year (Estimated)
CITING THIS RECORD
"United States Census, 1870," database with images, FamilySearch(https://familysearch.org/ark:/61903/1:1:MXXC-THB : accessed 19 May 2016), Levina Terrel in household of Asahel Terrel, Indiana, United States; citing p. 33, family 242, NARA microfilm publication M593 (Washington D.C.: National Archives and Records Administration, n.d.); FHL microfilm 545,806.