Well played, sir. Well played. 
I’m a huge Eagles fan and have been for a long time. I’ve seen them several times starting in 1975 (that lineup was JD Souther, Jackson Browne, Linda Ronstadt and Eagles), and the last was in September in NYC. I did not notice and could not tell that DH was lip syncing. In fact, he sounded as natural and as gravely as he always has. If he lip synched somewhere else, perhaps there was a reason. Who knows? I will add, Joe Walsh is fantastic on guitar!
Rock on!