I would do the following:
Use a punch to mark the drill hole from the inside, through the square hole of the lock.
Drill a pilot hole, again from the inside. In that way it should be perfectly centered.
Now drill from the outside a hole with the diameter you need. Use a step drill bit, so much better when drilling metal plates.
The one thing I do not know is how to fix the to screws of the door handle mounting plate to the door - whether you have the space to fit nuts inside or should use a parker screw. You'll find out.
