Is it completely safe to paint a lamp shade and use it or will the light bulb cause the paint to be combustible?

The keys will be
1. what material the lampshade is, and
2. what type of bulb will be used.

If you use a paint that is non-flammable then you will be safe... but if the bulb is incandescent, then it may "bake" the paint on the shade which may ruin it.

Regardless of the above, my thought would be that it would be easier and cheaper to just buy a lampshade that you like rather than try to paint the one you have.