Hake's "Collectible Pin-Back Buttons" gives a date range of 1928-1949 for that St. Louis Button Co. back. FWIW, it also lists a Geo. Lauterer back with 1906-1985 range, but with a different street address.
Dr. Muchinsky (springpin) could probably tighten up both of those dates considerably and will hopefully chime in.
Edit: And it looks like he did as I was looking things up and typing
