As to lecture title
No record is currently available for the title of the lecture Wilde gave in Racine, although The Decorative Arts was the one he was giving immediately before and after.
See also note at Dubuque
Building details unknown. But this is not the Blake Opera House built in 1882 that was destroyed by fire two years later.
Not a good week
Wilde was in the middle of eleven consecutive days lecturing in eleven different cities. He was annoyed that the wrong lecture title was being advertised—and this together with the smaller towns he was visiting meant that audiences were much reduced. He was also becoming physically tired:
March 1: he cut short his lecture to a small audience in Dubuque, IA.
March 2: he lectured again to a "comparatively small audience" in Rockford, IL.
March 3: he lectured again in Aurora, IL.
March 4: he lectured again in Racine, WI (this page).
Wisconsin was the third state he had visited that week, and he broke down during the Racine lecture before a small and unappreciative audience saying he was exhausted and unable to read his manuscript.
It was probably this incident that prompted Wilde around this time to write to his manager Col. W. F. Morse (Complete Letters, 146) in which he referred to the 'fiasco of the last ten days' and pleaded for a return to larger cities 'instead of wearing my voice and body to death over wretched houses here.'
Wilde did not stay overnight in Racine. After a hurried exit from his lecture, he traveled on to Milwaukee arriving at his hotel around 11:30 PM.