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.

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.

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.
Your post says "screen door" but it sounds like you want to change the sliding glass door and the screen along with it. Most glass door units are modular, the glass sections (stationary and sliding) are separate pieces and the track runs the whole width of the unit. If this is the case it may be possible to switch things around.
Take a good look at the unit, the sliding door should lift up and inwards for removal. Once removed you may be able to see whether or not the stationary units can be removed. Look for screws on the inside and outside that are holding the units in place. The stationary units can usually be lifted up and removed as well. If we represent the original arrangement as A-B-C (with "B" being the sliding door) you might be able to replace them in this configuration:
B-C-A.
The panels are heavy, don't try it alone. Prepare a flat area to lay down the sliding door so you can refurbish/lubricate the wheels while you have it off (I use sawhorses). Some old glass units are NOT tempered safety glass and could hurt you terribly if broken, be careful. The weatherstripping scheme, as well as the latch, may require some ingenuity as the setup will not be the same.
Not all glass door assemblies are made to take apart like described, especially custom stuff.
Best Answer
In a traditional panel door construction, the panels are held in grooves cut into the rails (horizontal pieces) and stiles (vertical side pieces). The rails and stiles are doweled and firmly glued together, and it is impossible to take them apart without ruining them. The panels are not glued in place, so they can expand and contract with the heat or humidity, without changing the overall dimensions of the door.
If you want to try to replace one of the panels with a glass or perspex pane, you must carefully cut away the molding from one side of the panel. (You should cut on the outside of the door because windows are traditionally caulked on the outside.) Remove the wooden panel and use a chisel and sandpaper to clean up the opening.
The steps, in cross-section:
Then you can install your pane using standard glazing technique.
You might also want to replace a damaged wooden panel with another wooden panel. In that case, instead of caulking you would install milled wooden strips, such as quarter-round or very small crown molding, to hold the new panel while allowing for expansion etc.
One problem you will have is figuring out how much molding to cut away. You should carefully carve material away, about halfway along one edge, until you can see the edge of the panel, then extend the measurement to the corners.
Alternately you may be able to break the panel and remove it without damaging the door. Cut out most of the panel with a jigsaw, notch the remaining frame almost to the molding in several places, and break out the remaining pieces. Once you have wrenched out the first piece, the others will come out quite easily. Then you can measure the depth of the groove directly and decide how much to cut away.
I would call this an advanced-level project, because the results of your carpentry -- joinery, really -- and your glazing will be highly visible and in your face every time you enter or leave your house.
If you have some artistic design or special effect in mind the results can be worth the effort. But if you only want to get some more light into the place, just buy a new door.