Set the lock into the stock, and clean up the edges of the oversized gap. Now, make a piece that will fit into the void, and glue it in with stainable wood glue.
Or leave the lock ouot, clean up the edges of the inlet, make a piece that fits tightly against the wood, and wedge it tightly there with the glue, and a wedge inside the inlet. Then re-inlet it to your satisfaction. It ain't over 'til it's over!
Don't use superglue or CA - it won't stain at all.