My mom just got a new iPhone 5s (16GB) and I noticed this issue on boot-up. Right after the white screen, the lockscreen shows up very briefly, like a nanosecond. It requires pressing the home button to bring it back. On my new 5s, the lockscreen remains there for a few seconds after booting up giving you a chance to swipe. I did a full restore twice, with backup. I did a reset with the settings. It keeps happening. By the way, once the phone is on, pressing the home button or top button brings up the lockscreen and everything else seems normal with the operation of the phone. I'm thinking it's a iOS 7 issue and maybe the 7.1 update could correct it. Then again, it could a hardware issue. Has anyone else experienced this issue?