I see that you posted under a carpentry tag. however, my solution would be to find a section of Aluminium Tubing, or tubing profile which fits the "gap" which you describe.
![enter image description here](https://i.stack.imgur.com/Nv85T.jpg)
As You can see, the example picture is a rectangular profile, which will run the entire height of the door, To fill the specified gap.
Your problem will be to attach said profile to the side of the slider. essentially the best thing would be to drill into the frame and insert pop rivets, however, there will be a glass pane on the other side of the aluminium door frame, so drilling will be difficult.
The profile below will allow you to drill your rivets on the side of the door (ie the narrow face of the sliding profile, then you can drill two holes on the top and bottom of the slider (in your photo its the side you can see.
You will then be able to mount your lock flush to the hinge door.
![enter image description here](https://i.stack.imgur.com/E6TAr.png)
Above you can see what I mean. I must stress here, that you dont want to break the glass pane by drilling into the frame where there is glass.
In case someone comes across this in a future search, here is what I did on a similar project:
First, I used an oscillating saw with a plunge bit to cut the nails—-much easier than a sawzall. I used little magnets to sweep along the face of the stucco mould and locate them, then I plunged in from the side to cut them. I cut the paint with a utility blade along the seam where it joined the frame and tapped the mounding free with a hammer & chisel (aka screwdriver).
Then I cut the door frame nails with the plunge bit from the front and back after locating them the same way. Since my door also had zero gap between the frame and the studs, I had to do some persuading with a hammer to move the stud where I wanted it, plus a slight trimming of the bottom plate with a hand saw. My header was also nailed out of level and I had to tune up the corner with an actual chisel.
Now, my stucco molding was 1” thick and they apparently do not make that any more, so it was impossible to replace (would have been easier to paint and reuse it but it was in rough shape). I had to go with the 3/4” stuff. I also went with a door frame that was ~1/4” wider to compensate (old was 4-1/4”, new was 4-9/16”). The shape of the channel turned out to be different as well, so I simply cut off the exposed lip of the stucco with an angle grinder with a diamond wheel. I also had to rip off the lip of the stucco moulding on my table saw.
I had to cut the top of the stucco about an inch higher to match the new, standard sized door frame I bought from the big box store. I used a grout blade for my oscillating saw to do the corners. To finish I used OSI Quad caulking between the stucco mounding and stucco and it turned out great, no need to repaint anything because I cut a nice clean edge.
As you can tell, I ran into every single nightmare possible! But I could see all of them coming, had the right plan and more importantly the right tools. I wanted to share my experience in case someone else is looking to do the same job. Good luck!
![Before and after](https://i.stack.imgur.com/6o3Id.jpg)
Best Answer
If you look on the hinge side of the door you may find a makers tag with a model number. If the door is fairly new the manufacturer may be able to supply a new one. You also might try a glass and window shop. The grid is typically screwed to the door. Small plastic plugs cover the screw heads. Some that I have encountered also have an adhesive applied. Sliding a putty knife under the grid will release the trim.