Any phone with a camera that can focus 20-30cm (8"-12") and with a flat face should work. Cameras with a protruding lens will generally not work from the top of the Lightcase but will work from the front.
We have tested many types of camera phone and just the HTC Desire HD had a problem in that it could not fit the full size of the background within the frame. The best way to confirm you will capture the full size of the background using your camera at the top is to hold you phone 310mm above an A4 or Letter sized piece of paper and see if the paper fits within the camera frame.
Some zoom lenses will fit others won't. The lenses that clip onto the corner of iphones will not work but usually lenses that screw onto a phone case or magnetically clipping lenses will work. The hole on the top of the Lightcase has a diameter of 19mm / 0.75 inches so a screw in lens fitting less than that should work.
You can also hold the smartphone inside the case and capture the object close-up.