For the impatient or TLDR ... Put: export LOCKPRG='/bin/true' in your .bashrc. Kill all screen sessions and start a new one. Ctrl-a x should now do nothing. Also, a nice fellow named Brian suggested I just unbind the x key. I thought it was a good idea. Just put "bind ^x" and "bind x" in your .screenrc. Lot's of different ways to do the same thing. Re-binding is the better way though.
I have been using GNU Screen for a while now. I usually create multiple new windows (Ctrl-a c) every day. Then I flip back and forth between the multiple screens (Ctrl-a n) or just toggle between the last 2 windows used (Ctrl-a a). Sometimes my finger slips and I hit Ctrl-a x which provides you with a password prompt. This is GNU Screen's lockscreen function.
Normally you just enter your user password and the screen will unlock. Screen is using /local/bin/lck or /usr/bin/lock by default. This is all fine and dandy if you have a user account password to enter. If you have servers that only use SSH keys and don't use passwords you will have no valid password to enter. In other words you are stuck at this lock screen. One way around it is to login to the same machine and re-attach to the same screen session (normally "screen -r" if you have only 1 session open). Then kill the session with the lock screen. This is annoying to have to do.
I wanted to be able to just disable the lockscreen setting and be done with this. Looking at the man page it shows there is no option to turn this off. So you have to go around it in a way. The way I found to do this on machines without user passwords is to disable the terminal lock program by setting the environment variable LOCKPRG to "/bin/true". For BASH put export LOCKPRG='/bin/true' in your .bashrc. Kill all screen sessions and start a new one. Ctrl-a x should now do nothing.
For security sake be careful about disabling your LOCKPRG. /bin/true disables all terminal screen locking, so if you use some program that uses whatever is in the LOCKPRG variable it essentially disables it.