First when taking pics from the lock screen it will, mine anyway, only show pics taken during this session. So for example you wake the phone, open the camera take a pic or two and then touch the thumbnail. A small gallery opens and shows you the two pics you just took. It will not show you the full gallery because the phone hasn't been unlocked. Another example is you wake the phone, take a couple of pics, put the phone to sleep, wake the phone again, take another couple of pics, then try to view the pics. It only displays the pics taken during the most recent session and not the ones from before, even though you didn't unlock or lock the phone in between. The phone won't display the pics of the earlier session because you can only view current session pics until the phone is unlocked.
As for not being able to find the pics, since you are using file names I will assume that you are using a file manager to locate the files. First go to your camera settings and see where photos are being sent. I'm not sure how many options you will have but often there is a choice between internal and external memory, but some may have options to save to cloud or a cloud service, while others may also have the option to direct the photos to a specific folder. You need to first determine where your photos are going to have an idea of where and how to look for them. I cannot think of any reason that you would be able to take photos and them not be saved. If it was a low memory issue it seems that you would be directed to either identify an new save location or reduce data to make room for the new additions. Without knowing what your settings are it would be pure speculation on my part to try and help you locate the photos and there are too many possible scenarios to attempt that. When you reply with your settings we can help you more.