Ok, here is one for everyone to chew on. In my household there is an iPhone 6 Plus, an ipad Mini 2, an iPad Air and an Air 2. On all of these you cannot swipe to delete email from the lock screen on ios 10. Like this thread says, you must open the message first and then delete it. I really hate this new behavior btw. Well I also have an old iPhone 5 that I use when I don't want to risk my expensive iPhone 6, or if I'm doing something and want a smaller profile phone, when I'm working outside or something like that. Anyway, I updated it to iOS 10 today and was working outside and I noticed while I was using it that it DOES have the option to delete from the lock screen! I can't find any setting that seems to enable it, and I confirmed that all my devices are running the same (10.0.1) version of iOS 10. I don't know why it is there on the 5 and not on any of the others. I'd sure like to figure it out.