Insulating Existing Walls with Lathe & Plaster, Wood Siding, and Stucco
To me, a moisture barrier is on the exterior of the building and a vapor barrier is on the interior of the building. Vapor barriers should not have a perm rating of 1 or less because trapped vapor in the stud space needs a way to escape back towards the heated side (or air conditioned side in the summer.) Moisture barriers should have a perm rating much better (lower number). Moisture from inside the building will migrate towards the exterior. After you install wall insulation, moisture will turn from vapor to water at the dew point and end up in the wall cavity. That's why it is important to completely fill the wall cavity, giving less air (vapor) to turn to water. 

So, on the interior face of the wall, it's ok not to have a vapor barrier, because any moisture that does get in the wall will need a way to escape. On the exterior side of the wall a moisture barrier is a must, because you want to keep water out. (this isn't just a little vapor trying to enter the wall.)

The exterior stucco could be an EFIS System if it's 2" thick and it should have a vapor barrier. If it's stucco, then it should have a vapor barrier too, but needs to be verified. (Probably 2 layers of building paper.) if the "exterior stucco" you call it is helping keep your house cool in the summer, then it's probably EFIS because it has a layer of insulation board in the system. 

I don't think you can use anything other than foam insulation in the wall, because you need to make the insulation go "up" due to the diagonal bracing. However, remember the entire stud space must be filled. You'll need to drill holes at the top and bottom of the wall due to the diagonal bracing, which brings me to the most difficult issue: drilling through the stucco or EFIS system. 

Patching stucco or EFIS is difficult. Stucco probably has a metal fabric layer that will be difficult to cut through without ripping the stucco apart. Stucco and EFIS should be patched by a professional. If you mess up patching these systems it will leak and you'll have a mess. Don't try it yourself. 

The plaster in the lathe and plaster system may have asbestos. You can get a kit and send a sample off for testing. If positive, be sure to protect you and your helpers. (By the way the asbestos fibers will linger for days and land on everything in the room. Clean up involves cleaning everything. Use plastic drop cloths and toss when done. Asbestos companies use fans in windows to create a negative air pressure so you're not blowing asbestos around the neighborhood. ) I recommend a licensed abatement company if you have much to remove. Plaster can be patched, but you may develop cracks again. I'd add a layer of 1/2" gypsum board if the studs are 16" oc. 

By the way, don't forget to vent the attic when you add attic insulation.