Don't knock out the hole until you verify that the holes in the handle line up with the lock lined up with the mortise.
I would slide the cylinder into the handle (without the hole punched) then insert the screws through the door into the pull. If they line up, great, punch out the handle.
Thanks for the response!
There is another problem that we're having with the door and that is that the latch isn't seating correctly. The latch wasn't hooking in to the bracket on the jamb. I tried adjusting the position of the bracket, fastening it a little lower on the jamb, but then the latch won't function. The only way to get the latch to work now is to close it half way with the door open and then close the door and finish closing the latch. I'm afraid this will mean that a key won't close the lock. I'm wondering now if the solution is to buy an entirely new door handle that has a keyed lock installed? What do you think and can you tell me what the part # is for that based on the photos above?
Put the hook in the locked position.
Move it up close to the strike.
Try moving the strike up until only about 3/16" of the hook goes inside the strike (sometimes less).
The instructions usually say to line up the strike much lower.
It never works that way in my experience.