As a Lorain Baby Boomer, I remember this City Hall well. I drew it during a 1968 Saturday morning art class (which I blogged about here.) About two years later, I paid a visit to the police station behind City Hall while working on a science project (remember those?) on forensic science. (Columbo was on TV at the time and it seemed like a good topic.)
Now for a little history. According to a Journal article from the 1970's, at one time the building was one of the finest mansions in the city. It was built by William Jones.
In 1877 it was purchased by John Stang, a prominent citizen, banker and landowner. In 1903 the City of Lorain bought the house for use as City Hall after a fire destroyed the building which previously housed the city offices. The building then served as Lorain's City Hall for 22 mayors, until its demolition in March 1974.
Here's a link to Loraine Ritchey's website, where she has a nice collection of vintage photos of the original brick building, as well as a few with the later peeling yellow paint.