I am interested in adding some insulation to a wall that will be gutted while repairing storm damage.  The exterior wall on our house are stucco on wood lath. On the inside side of the lath there is tar paper.  The lath serves as a a sheathing and a lath. 

Would it be a bad idea to put insulation in these cavities directly or should I follow the procedure for foam board with an air gap for uninsulated walls?

The house has pretty substantial overhangs of 27 inches that for the most part keep it dry.  I have attached two pictures of Byrkit lath for reference.