If you know what make and model it is sure..I mean, is it possible just to replace the handle bit instead of the whole bit including the one that is currently screwed to the door?
If you know what make and model it is sure..
Or, you might find a handle similar enough that can be taken apart and or modified so the L shape fits on the plate you have, so that screws line up etc
If you have a decent set of tools you may well be able to repair what you have by fixing it to the square rod each side (eg drilling a hole through handle and rod, tapping it out and using a grub screw)