Graphite powder is the best but as your supply could be limited then the pencil is a good secomd best.

Rub the "lead" against an abrasive paper,

medium grade,

then contrive a delivery method.

The graphite powder comes in a squeezy bottle so the nozzle can be placed into the lock then puffed in.

And you cant get to much in,

Graphite is very soft so it lube as it's crushed.

Some on the key blade too then insert in remove and repeat.

This ought to lube the little springs and wards in the lock,

Never had it fail,

Unless the internal are very worn then the answer is obvious.

I`ve never found WD-40 any good for locks,it lasts a short while then makes the lock worse,but if the key won`t go in

I strip the lock then clean with either petrol or parafin, once dried, grease with lock grease then put back together-should last for life after that. not difficult to do