I read with interest your query about Iver Lybeck. I am also a descendant of Iver Lybeck. My grandmother was Maren Lybeck, younger sister of Johanna. From the information I have, Iver, Karrin (you have Karen), Johanna, Hans and Maren came to the US in 1869 and settled in Lewiston, Wisc., where a brother, Andrew, was born in 1870. At some point they moved to Faribault, Minn. Later, I believe in 1900, Iver, Hans, Maren and Andrew all settled around Fillmore, ND. Iver Lybeck filed for land under the Homestead Act in both Wisconsin and North Dakota so there is quite a bit of information you can get from the Bureau of Land Management. They will send you copies of everything they have for a small fee.
I have an old post card that was sent to my Dad from Valley City, ND, dated 1918 that was signed by Luella so I'm assuming the cousins were in close contact at some point. She mentioned Norman driving the wagon she was riding in while she was trying to write.
Hope this answers some of your questions. I am very pleased to have found information about Johanna's family. Any other questions, please feel free to E-mail me.
Dorothy Thorson