I have lived many years in Lorain, and have never heard of a Dr. Frederick's Hospital. As far as I know St. Joseph's Hospital founded in 1892, was the only hospital in Lorain in 1912. I have copies of local histories of Lorain published in 1903, and 1916, and neither mention a Dr. Frederick or his hospital. However, next week I will be at the local library, and will check the Lorain city directories from 1912, for a Dr. Frederick or a hospital. I will let you know what I find.