A basic technique of using the index in Ancestry is to put in the father's last name as the name you're looking for and then enter the mother's last name in the Family Member field. I leave all other fields blank. The index will display every entry that matches the combination.
In my case, I had neglected to cross check the father's name Lobdell with the mother's last name Booth. When I did that, lo and behold, I had two matches that gave me the father's full name plus the mother's middle name.
Herbert Edward Lobdell and Margaret Pauline Booth were the parents of:
Yvonne Lobdell b. and d. 20 Jan 1936 in Wichita Falls, Wichita County, TX (FAG 52932259)
Marcia Jean Lobdell b. 8 Jun 1937 Wichita County, TX
Now it's a matter of trying to chase down more information on each of these people.