A 'complete 2-hour video' of the event is offered on the web, but I'm not sure if Ray's tribute is really part of this (the Columbus Times wrote: "Sorry you will not eye or ear these side events on the tube rebroadcast...").
There's also a video containing parts of that 1986 event (including a biographic documentary), and an October 2003 performance by Ellis Hall - at the request of the ailing Ray Charles, who had recently been co-producing an Ellis album on Crossover Records. Watch it here (requires RealPlayer). And don't miss this photo. Some more fragments of the same '86 event, Ellis' 2003 act, and more promo stuff from Ellis are here (again with a confusing timeline;-):
The 1986 program was announced as "An evening of tribute and entertainment", first from the White House, then the Kennedy Center. It took place on December 7, 1986.
Below is the - seemingly complete - footage of the tribute to Lucille Ball. In Part 1 Walter Cronkite introduces the honorees and shows a recap of their evening at the White House. Ray, sitting right next to Lucy, is on camera a lot in the other parts as well. Reagan's speech can be watched here; national anthem here.