If you are going to include a light or light mesh with a background image or EZDome to provide additional fill-in illumination, you should closely match the light color, intensity, and light direction for a blending effect.  Otherwise, the scene will just not look right.  For the longest time, I have been working on a scene, reconstructing shader nodes for Superfly, and recasting props throughout the scene.  Initially, I started with an EZDome but switched to an 8K HDRI that was rescaled to 4K.  I followed the background shader setup posted above, rotated the image to my satisfaction, and rendered the first image with ambient lighting.  

The second image that follows contains 1 infinity light, set to a 25% intensity, shadow intensity to 85%, Shadow Radius Blur to 4, and the light color to match the background.  The direction of the infinite light matches the direction from the background ambient lighting.

The inclusion of the infinity light brings out the specularity in the scene, a situation that you don't see with the ambient lighting from the dome or background.