Under iOS 8, there are a couple of steps you can take to handle emails right from your lock screen if you want to send them to your trash or mark them as read. Doing this involves swiping across an email’s notification when it appears there.
If you swipe from left to right (in the direction of my green arrow below), you’ll need to unlock your device, but then you’ll jump right to that message within Mail.
From there, you can reply to it or what have you, so that’s a convenient way to go where you need to. Even more awesome, though, is the fact that if you swipe from right to left (like my red arrow above), this is what you’ll get:
Obviously, you can tap to send the message to the trash (for which you will have to enter your passcode or Touch ID) or mark it as read, but what about that tiny little “x”? Well, touching that removes the notification for the email from your lock screen without affecting your inbox at all. So if you’ve gotten an email you’d like to keep private, you can choose to deal with it later without having it appear if someone wakes your device up. Handy! And helpful for those of you with embarrassing friends. We know who we are, right?