This is my exact same problem. I never had this problem until I updated my phone to iOS 7. Now, I don't get any text alerts on the lock screen or any text tones. I've done hard resets. I've erased my phone and reset it and then restored with a back up. I've reset all my tones to default. I've tried changing notifications, changing it from banners to alerts. I've tried taking notifications off and then back on. I've tried everything I can think of. Nothing fixes it. This is driving me crazy. My children communicate with me by text and I can no longer depend on my phone to alert me to their messages.
I had exactly the same problem. Just rest the phone (Held down power button and home button until screen went off and until the apple appeared).
When it came back on, good as new.
I think its safe to say that ios 7, as good as it is, looks and feels, still has some slight technical bugs that need fixing!!
Check your settings under do not disturb. Mine was set to manual and a little moon was displyed near the location symbol at the top of the screen. Once I disabled that it's been working fine.