I have a set from Weber installed on mine and the cover fits fine. Mine have the same handles as are on the lid. That said, making them yourself is simple. Somewhere on this site there used to be a complete tutorial on how to build a set if you have the plastic handles. It just takes getting a strip of aluminum from someplace like Lowes, drilling a hole for the center handle screw, then bending around the handle to form the "legs" and then choosing the length of the "legs", and bending them outward to get the flat to drill and mount. I know it sounds difficult, but it is really easy because the aluminum strip bends easily and can be cut easily with 9 inch lineman's pliers.
At any rate, yes, the original cover fits fine unless you make the handles too tall.