On what date was the album featuring the song Perfect Illusion by Lady Gaga released?
Perfect Illusion:  It was made available for digital consumption on September 9, 2016 through Interscope Records as the lead single from her fifth studio album, "Joanne" (2016). Joanne (album):  It was released on October 21, 2016, by Streamline and Interscope Records.
October 21, 2016