I know that it has been quite a while since your message was posted, but I was excited to read your posting. My husband's g-g-grandfather was Jacob Peura who settled in Cromwell. I have his daughter's name as Laila, not Lila, but I may be wrong. Here is the info that I have on him:
He and his first wife Gustava and two oldest children William H. and Hilma K. immigrated to the US around 1892, and lived in Maple, Wisconsin. They had another daughter Tekla around 1902. Sometime between 1902 and 1910, Jacob's first wife died and he remarried Anna. Sometime between 1910 and 1913, they moved to Carlton County, Minnesota, and they had a son Brunnolf around 1913 and a daughter Laila around 1914. Jacob Peura died on February 23, 1944 in Carlton County, Minnesota.
Hopefully, this helps. I'd love to hear any other information you have, too.
Traci Nyberg
tracinyberg@ou.edu