I gave a crack at this because I love lighting situations. I approached it from a physically correct perspective, which is not always what makes the best stylization, but here's my reasoning process for determining lighting like here. I'll add that this was quite a difficult study (as soft light sources tend to be compared to hard light) and I'm far from happy with the result. I feel like I could be quite off. For a proper study I'd model this in 3D, but I wanted to do some sketching so you get just my best guesswork.
The top image shows the assumed lighting: the sun is high, but from behind the building so no direct sunlight is actually going into the building. Therefore, no hard light directional light sources inside the building. All you have is the sky, which is the blue wavelengths of sun rays that got scattered through the atmosphere. For an early afternoon situation I'll just assume it's radiating equally blue from all top half hemisphere.
Now, to determine how bright any spot in the scene will be, you have to imagine you're in that spot and looking around you, 360 degrees. And then the bigger part of your field of view where you will see the sky, the brighter that spot will be. So if you sit right at the door on the floor (imagine you're an ant), all your view in front of you will be the sky. As you go more and more back into the building, the wall is starting to obstruct your view of the sky, so less skylight is shining to that location. So the more you go back, the less light you get through the door. At the very far end of the room the door covers a tiny fraction of your view, but it still covers some—it isn't going to be completely dark/unaffected. In your take the light basically affects just a tiny area around the door where in fact the light will gradually fall off towards the very far end. It falls off quickly at the start and then slower and slower.
I also played around with windows a bit, where the situation is similar, except that as you get close to the bottom of the windows you again get in shadow since you can't really see much of the opening of the window if you're an ant right underneath. So it also fades toward the front wall.
Here's my attempt at lighting the room (just the door) with all this in mind:
It's relatively correct, although, like I said, doesn't immediately translate well to a pixel art scene. But if you look at real photos of lighting situations like this, you'll see that the general idea is correct.
How to stylize this best for pixel art? Well, that's a different issue. It really depends on your graphics engine/palette/art style limitations. What I can say is that the gradient will be easier to produce (or mask), even with a limited palette, if you have textures in place. Then you can gradually step down your ramp, for example, as you transition from plank to plank (if it's a hardwood floor). If not, the best you can do is to just have a very bright ambient light and only do a small gradient right next to doors/windows. That's what you'd usually see in a tile-based top-down RPG.
Very rudimentary example of the concept:
Again, when textures and items are in place, this would look better. Like here in Crossing Souls: