Since i played with 2D Sprites and Tilesets for myself at the weekend, here is how my described version with separation into background and foreground can look like:
I used UE4s Paper2D and followed this tutorial:
i just changed the Paper2D sprite materials from an unlit to a lit version (and let them cast shadows), and added an emissive slider for making it visible even when no light is nearby. Thats why the lights affect the background. Just have to figure out, how to let the player sprites cast shadows too.