This is an Emerson (John Haven Emerson, 1906-1991) iron lung, an improvement on the Drinker design. It seems to have been Memorial’s second adult-sized iron lung; the first one was a Drinker model donated in 1931 shortly after the gift of the baby respirator. The slide-out bed and portals in the side that allowed nurses to attend to patients without removing them from the lung were Emerson innovations.
Iron lungs were expensive—this one would have cost around a thousand dollars, and the earlier Drinker model almost twice that—and still relatively rare in the 1930’s. Note that this one was also funded through public donations. See more at ic-103.pdf.

Founded on September 1, 1907 as the Baptist Sanitarium, Memorial Hospital began as a two-story, wood-framed building at the end of the trolley line on Lamar and Smith. It had 17 beds and eight trained nurses on staff. It was the second general hospital established in Houston after St. Joseph Hospital which opened in 1887. It was also the second Baptist-supported hospital in the United States.