LightMtl with "emit light" off is invisible to the GI (does not cast shadows, generate light, etc), and that's why AO is not working with it.
If you need such exotic setup (for any reason), use RaySwitch material and plug the LightMtl with emit light off into the direct visibility, and plug any shadow-casting material (such as standard Corona Mtl) into the GI slot. This way it will magically start casting shadows, will not generate light, and the AO will become visible.