Since 2013, the Alvin Ailey American Dance Theater has appeared annually at Lincoln Center's David H. Koch Theater. This year is the exception, somewhat. As part of its Ailey All Access series of online presentations, begun March 30 in the wake of the pandemic, the troupe has been working on ways to still offer a June season of a sort. Before the theater shutdown, live performances had been scheduled for June 10 to 14. Instead, starting this Thursday at 8 p.m. EDT, viewers at home will be able to stream a four-part mixed bill, performed on the Koch stage, the was filmed in 2015.