The State-Lake was a sister theatre, albeit an older one, to the Chicago Theatre across the street. In 1985 the building was gutted and turned into the WLS-TV studios.
According to the Jinx 25, Harry Blackstone played the State-Lake Theatre in Autumn of 1936. In the Sphinx, Blackstone was also playing to sold-out crowds here in May 1940.
Link: State-Lake Theatre at cinematreasures.orgCourtesy of Potter & Potter Auctions State Lake Theatre