Lesson #1: The days of recording a song, letting it sit for a few weeks—or, worse, a few months—and then putting it out and promoting it are looooooong gone.
Really, this isn't a lesson that Jay in particular taught us, but his situation does shine an even brighter light on it. For years now, rappers have recorded tracks, sat on them for awhile, and then tried to released them and build a lot of buzz around them when the timing felt right and their albums were finished and ready to drop. In recent years, some artists have done away with that approach by dropping songs almost immediately after recording them. But in Jay's case, he literally let folks know he was working on something, worked on it, kept them updated, and then put it out for everyone to hear.
Rap fans have become obsessed with "The Making Of..." pieces about how rap songs and rap albums from the past came together, and Jay basically just took it one step further. He let folks know how he made a song by letting them in on the process and building a healthy buzz for a song on the same day that he was both recording and releasing it. Rap fans have shorter attention spans than ever before, so this worked out perfectly for him and could help other artists interact with their fans and release new music as well.