Here’s that McCollister family again. I still didn’t find a record proving this Lillian married your Pete H. Petersen but there are a number of facts and records that suggest a possible connection. I looked into it because of an Ancestry.com “hint.”
The census says Lillian Petersen’s mother was born in Alabama, and that is where Mrs. McCollister was born:
1910 Kilfoil, Custer, Nebraska Geo S McCollister 34 Anna McCollister 32 born about 1878 in Alabama Cleda McCollister 11 Alfa McCollister 8 Ivis McCollister 6 Lellie McCollister 3 [ = Lillian]
1920 Ansley, Custer, Nebraska Stanley G Mccollister 43 Anna N Mccollister 41 born about 1879 in Alabama Alpha C Mccollister 18 Iris R Mccollister 16 Lillian E Mccollister 12 Martha C Webb 26
1930 Ansley, Custer, Nebraska S. G. McCollester 53 born about 1877 in Nebraska Anna N McCollester 52 born about 1878 in Alabama; parents b in Tennessee
1940 Ansley, Custer, Nebraska Stanley G McCollister 54 born about 1886 in Nebraska [age 64] Annie McCollister 63 born in Alabama Harold McCollister 14 grandson
Harold’s father Alpha McCollister is in Portland, Oregon, in 1940; in 1930 Alpha and wife and children including Harold are in Mason City, Custer, Nebraska. Harold died in Oregon. An obituary for Harold R. McCollister, age 83, of Ansley Nebraska, died in Beaverton was published in the Oregonian 2009-10-4.