Sun lamp and background image with LuxRender

I would like to recreate this scene:
Right now, i have this in Blender:

I’m using a Sun Lamp with “Sky only” option to light the scene. Now I would like to insert a background image in Blender for the landscape outside the window, but I would still like to use the sun lamp to light the scene, independent from the background image.
How can add a image in the background so that it appears undistorted?
I want to control the lighting of the scene with the sun lamp, independently from the background image. The background image should not contribute to the lighting of the scene. How do i set this up? I’m using LuxRender.