Lara....Using the names of Lillie's siblings which weregiven in her obituary (obituary sent to you privately), this appears to be her birth family.
1910 Delaware Township, Wyandotte County, Kansas Census - ED 145, Page 31A - Enumerated 12-13 May:
Andrew K. Peterson, head, 40, married once/20 years, b. Sweden, parents b. Sweden, immigrated in 1890 (not clear), naturalized, farmer
Emma H. Peterson, wife, 45, married once/20 years, has had 10 children/8 living, b. Sweden, parents b. Sweden, immigration same as Andrew's
All children were born in Kansas.
Harvey C. Peterson, son, 16, laborer/home farm Ruby O. Peterson, daughter, 14 Lilly V. Peterson, daughter, 12 Earnest G. Peterson, son, 7 Ester O. Peterson, daughter, 6 Andrew H. Peterson, son, 3 Gladys Peterson, daughter, 1-5/12 ------------- Will try to locate additional records.If I do, I will send later....Pauline