Can I place my locking nut on a non-floyd rose bridge? I have one but I don't have my bridge anymore.
well you can, the locking nuts are usually bit bigger than regular nuts though, so you would most likely need to widen the hole for it. Also I don't think it would be much of an improvement (unless your guitar has huge problems with tuning stability), not to mention the pain of unlocking it each time you'd need to re-tune (since you don't have fine tuners at bridge)
I can't see any reason to modify your existing nut hole, especially if you have a fixed bridge. Much as Koryi said, unless you have massive tuning issues it would be a pointless exercise - and even then perhaps you should be looking at repairing / replacing the guitar rather than applying what is essentially a band-aid solution.