It doesn't even have to be a fib about a mechanical problem. You already mentioned busy and conflicting schedules- can't you be busy at that time? It doesn't even have to be a lie- schedule some "me" time, read a book, or catch up with a friend. Just because you're in a relationship with him doesn't mean you have to be available to him all the time.
Pan Female, Hinge in a V between my mono (straight) husband, Monochrome and my poly (pan) partner, ThatGuyInBlack