I would go with a patio cover with real roofing of some kind. The lattice is useless. It won’t provide cover from the sun or shelter for your outdoor furniture,

This is a good idea. Usually people want these things by the rear sliding glass door. It is better to actually protect this area of the house from the elements for preservation of the house,comfort and cleanliness.
If you go with lattice put a rain shield of some type over the first few feet around the door(if there is a door).