I haven't seen a lock retaining screw that is as large as a 3/16 inch (#10) thread on any rifle or musket.
I usually use a #6 (.138) or a #8 (.164) screw to retain the lock on the guns I build.
It would be a good idea to take the lock to a hardware store that sells screws and try out the ones they have on hand to find the one that screws in easily.
If you can't find a screw that fits, ask someone in the store if they can check the thread size for you. They should be able to do this.
Chances are good that the screw has a metric thread on it if the gun was made in Italy or Spain.
In the meantime, maybe someone on the forum has the screw your looking for.