The basic pin tumbler lock should work ideally with only one key.
Remove screen door lock without key.
Pull the door up until you can see the bottom wheels on either side.
Then use your screwdriver to unscrew the head stop located at the top of the door frame.
To accomplish this you can either make use of raking or single pin picking.
Look for a small set screw at the base of the handle.
This is a quick video to show you how to replace a sliding screen door lock.
How to remove a door lock without a key.
To remove a sliding screen door find the screws at the bottom corners and unscrew them with a screwdriver.
To do this when door is open you will need to press the deadlatching pin which sits above the main latch next you will need to undo the cylinder retaining screw.
Unscrew this plate and remove the latch from the door if possible.
Remove this screw using a drill or screwdriver.
That is unless you have a master key system in place.
So in order to unlock a door without a key you will have to imitate the action of the key itself.