How to remove my lock so I can try your 82-225

Unfortunately, I don't think the 82-225 is going to work on your door. The 82-225 is generally used in older surface-mount handle sets; that is to say, handles that have the latch (the 82-225 in this example) built into the handle itself.

That's not the case for your door. Your latch is built into the door, and to be honest with you I have no idea what it could be. I've never seen this design before. I'm guessing that it's fairly old, given that it's an aluminum frame, but that's about all I can garner.

Would you happen to know the manufacturer of your door? That may help me track something down, but right now I cannot tell you what your old latch might be, or even how to remove it. I've just never encountered this door before. My best guess is that partial disassembly of the frame will be necessary. There appears to be a kind of "cap" that runs the entire length of the side of the door. That would presumably have to be removed first. You should check for screws that might be holding it in place.

Sure, if you don't mind drilling some new holes, then that's probably going to be the most direct solution to this repair. I'd suggest the 82-005. This is a very versatile handle set that I've personally installed on an absolute ton of older doors. It has its own mortise lock built into it, so there's no need to worry about whether it'll be compatible with whatever's in the door now (which you can just ignore). 

The catch is that it has a 4-15/16" hole center spacing, which is somewhat uncommon. If yours doesn't match then you'll need to drill new holes in the door to accommodate. You'll also need to drill new holes for the keeper, which needs to be mounted on the frame in alignment with the new latch. This will be either very simple or a little tricky depending on the nature of the frame itself. Some frames are more generous than others in terms of how much space you have to work with.