Moving back in time, the first record I find for Lily is the US Federal Census from 1910. At that time she is 12 and living with her sister and brother-in-law, Jennie Westerlin Carlstrom and Charles Carlstrom in Omaha, Nebraska, with their three sons, Harold, Roy, and Francis, ages 4, 2, and 7 months. Charles and Jennie were both born in Sweden, but again Lily is identified as born in Nebraska. Charles, who is was 38 at the time of the Census, is listed as having immigrated in 1883, or 27 years before, when he was 11. Jennie, who is 26, is listed as having immigrated in 1891, or 19 years before, at 7. This is also consistent with the family having come to the US (and specifically, Nebraska) before Lily was born in 1898.
Here is a good site for some additional information on Omaha in 1910 and before, including some interesting maps and photos.