By airway bougie, you mean the standard blue one, right? I just tried this with confidence today and to my dismay, my anesthesia tech was unable to pass a 37Fr DLT over it with lube. I just put in SLT instead and exchanged it. Later, I noticed the blue bougie I had used was 15Fr. Perhaps they're not all the same size or you all were using a bigger DLT? Upon review, sizes 37, 39, and 41Fr will accommodate a 14Fr AEC, but a 35Fr will not. It seems reasonable therefore that a 37Fr DLT may not accommodate a 15Fr bougie, but perhaps larger ones will.