Received a response from Kathy Headley, president of the Chicago Lawn Historical Society, regarding this building:
"In answer to your question about the building at
63rd and Central Park, I found that in the 1930s when the originial station
on the west side of the railroad tracks was demolished to allow for the
elevation of the tracks, this new 'modern' station was erected east of the
tracks and is indeed the same building as had the restaurant. The photo I
have attached is from 1938."
(I can't seem to get the Flickr photo thing working, but here is a link to the photo):