Lenk's Hill was bounded roughly by the downtown area, Swan Creek to the south, Dorr Street on the north and Junction Avenue on the east. It was named for Peter Lenk who owned a brewery at Nebraska and City Park Avenues.
My grandparents, and their parents, lived on Lenk's Hill and they used to call it "lower town". It was an area of mostly German families.
You may want to check your library for a book by Philip Luetke entitled "Voices From Lenk's Hill". The call number is 977.113 LEU and was published in 1995.