If yours is the same as mine (1926 building in Hollywood, CA), the tar you see is from tarpaper that has long ago disintegrated. The laths should have beveled edges. The tar paper went up on the studs, followed by the beveled lath with the narrow edge against the studs to make a space that looks like /__ that to form a key to hold the stucco in place. Then comes coarse chicken wire over the lath. Real stucco is just portland cement used as plaster. For real expertise in this area, check www.ornamentalplaster.com.