HD has a problem with some of it's molded saddlebags. The latch is molded into the body of the bag lid as one piece, HD only offers a full bag replacement as the repair option. This is on a 2004 HD Road King.
Step 1: The Broken Latch
It this case the part that broke was the place where the cable attaches, breaking off an ear. I used a yellow cloth to provide contrast.
Notice that the cable has a shoulder on it and also has a retaining clip withing a grove on the cable barrel.
Step 2: Make a Piece
I made a back up plate to attach cable barrel to. I used a piece of stamped aluminum out of an old storm door bottom. Bent it into the correct shape and drilled the correct size hole for the front part of cable barrel into with the shoulder firmly against the back up plate.
Step 3: Put It Back Together
Basically you need to make sure you have the correct amount of washers to accommodate the difference in thickness of the new bracket, in this case 3.
Slip the retaining clip into the grove to lock it all into place.
Slide the new piece into place and drill holes for pop rivets. secure cable with a bit of foil duct tape.
Step 4: Wrap Up.
This is just one way of making the repair. Each latch will break differently and require a different approach.
I did not go into detail about how to take the latch apart, I'm assuming you have some sense and can figure it out, if not there are several great resources on the net, look it up.
One of my other favorite tools is epoxy putty, which makes super repairs when nothing else will do.