One new notification feature in iOS 10 is the ability to reply to messages directly on the lock screen without a passcode or Touch ID authentication. This default settings may not be desirable to you due to privacy concern.
To disable, go to Settings > Touch ID & Passcode. Scroll down to “Allow Access When Locked” section and locate the switch “Reply with Message” and tap to turn it off. You will no longer be able to reply to a message on the lock screen without a passcode or Touch ID.