1) Curve Modifier
For a simple sphere, I guess using the Curve modifier would be the best solution:
- Create a bezier curve with the same circumference as your sphere
- Add a modifier to your ornament and choose the curve as your Object in the modifier
2) Surface Deform and Shrinkwrap modifiers
But as your shape is much more complex than a simple sphere, perhaps you could use this method:
- Create a plane, subdivide it and place it behind your ornament,
- Give your ornament a Surface Deform modifier, choose the plane as the Target, and bind it so that the plane will deform the ornament as you want.
- Give to your plane a Shrinkwrap modifier, and choose your lamp as the Target so that the plane sticks to the shape and the ornament follows.
- Disable the eye icon in the Shrinkwrap modifier and shift D > duplicate both your plane and ornament all around your object, according to the direction of your shape's normals.
- Re-enable the eye icon for each Shrinkwrap modifier so that you can see the the ornaments sticking all around your shape.
- Apply the modifiers you want, delete the planes.
- As this method didn't use an array, your ornaments are not properly joined, if you need to do it, join them with ctrl J and use some W > Bridge.