From the record
“The Lava High School Gymnasium, at 202 W. Fife in Lava Hot Springs, Idaho, was built in 1934.”
Wikipedia article Lava High School Gymnasium, CC BY-SA 4.0.
One of 30 National Register listings published here for Bannock County · listed in 1997 · category: Building · built in 1934, Neoclassical architecture, by Miles Miller.
Sources: the Wikipedia article · the case file at the National Archives · the National Register database, National Park Service