Not sure what you mean by composition siding, but if it is 4x8 sheets, they will be able to lath over it. Corner, eave, opening trims are removed, the siding fasteners checked to see if they need tightening, then the underlayment, flashings, weep screed- lath process.Here in the mojave desert there are two lath processes that are basically used. The first is a two ply underlayment "felt" applied over the weep screed/flashings and followed by lath wire. The second is a layer of 30# felt followed by 3/4" tongue and groove styrofoam panels over the weep screed/flashings follwed by the lath wire. The second eliminates one coat of a 3 coat process- scratch coat, brown coat, followed by the color coat either textured or smooth. You mentioned your area on your roofing post of arizona being pretty chilly in the winter and fairly warm in the summer. I would inquire about the acrylic color coat being used in those conditions. It remains pliable and expands/contracts w/ the temperature changes equaling less chance for cracking. We went that route on our build in the sierra nevadas where it averages 90's in the short summer months, and cold snow and wet in the winter.One thing to inquire about and is mandatory in calif., after the scratch and brown coats are applied, it has to sit a minimum of thirty days in order for those coats, (or coat if using styrofoam), to crack and somewhat cure before the color coat is applied. Very important as if not allowed, the scratch/brown coats will continue to crack if the color coat is applied to early and will protrude through the color coat. Another important step is to keep the scratch/brwon coats dampened 2-3 times a week, more if hot weather, during the thirty day period. The acrylic color coat can be textured in a wide variety of patterns or smooth. One more thing about the lathing part of the show, make sure the corners of window/door openings are reinforced with a patch of rib lath. It just gives a little extra "bite for the coats as those are areas where the structure can flex more than anywhere else.

That's great info. Thanks. By "composite" siding, I means its a man-made product. Its similar to hardboard but moisture proof and I think it has some cement in the binder because of the raw color. Its about 7/16 thk. The stucco guy said it should come off.

Im sure you have thought of this but you might want to get some convience items in before lath /stucco such as extra exterior receptacles, lighting, hose bibs,etc.

We resided, insulated, new windows, and Tyvek. What a difference in noise. We also increased our square footage by 25%. With the changes to the 'old' house siding our utilities have stayed the same with the same equipment.