Lubricating your screen door lock will preserve it and make it work smoother. Although they are designed for external use, the internal parts will corrode over time. It's essential the correct lubricant is used and applied where needed if you want to keep your door locking effectively.
What lubricant should you use?
I recommend INOX MX3 spray lubricant. From the manufacturers website:
MX3 is an anti-corrosion anti-moisture lubricant designed to be sprayed on surfaces and between moving parts. The lubricant is made with a high grade white oil, rust inhibitors and other components to give lasting protection from corrosion and oxidation. MX3 will penetrate through bolts and parts that are stuck together to help loosen and easily free up without causing damage.
CAUTION!!!
Definitely do not use a degreasing product such as some of the WD40 products as they can remove grease and oil which is undesirable in the long-term. Avoid graphite lubricants which will clog up your lock if used incorrectly. Graphite is only used in very specific circumstances for locks that usually require disassembly for servicing - not for the DIY'er
Where to Apply the Lubricant?
Keep a spare cloth handy to wipe up any excess. Only spray lubricant in a well ventilated area, use personal protective equipment, and consult the manufacturers safety data sheet before use (available on their websites). Spray liberally:
The collar of the handle
Inside the lock body through the lubrication holes or in one of the gaps at the latch
Inside the keyhole
Other Hints
If lubrication fails, there may be an obstruction on the frame which is preventing the latch from fully entering the strike hole. Filing down the strike or chiseling out some timber may help. Check alignment to see where attention is needed.
When testing your screen door lock, make sure the smaller "latch" is pushed in as the lock won't work without this "activated".
If your key wiggles in the keyhole, it's probably time for a new screen door cylinder and the broaching is likely worn.