If not lit, use different texture

What to recommend here is highly dependent on the larger context of your app. It is possible to do something like you describe with a shader (though you'd have to write it since I cannot think of one posted on the net that already does this), but simulating the light using distance and angle calculations may also be a solution. it all depends on the needs of your app.

In your shader, use a dot product to determine at a most basic level how much light this square is receiving. You want the dot product between the light direction and the surface normal. Something like this:

 if(dot(normalDirection, lightDirection) != 0) {
     //this area is being lit at LEAST a little, so make it red
     return half4(1, 0, 0, 1);
 } else {
     //not getting any light, make it white
     return half4(1, 1, 1, 1);
 }

The dot product will be 1 for total light exposure, and 0 for none. Values inbetween are varied levels.

This is a super crude example, but what you want to do is entirely possible if you are willing to write a custom shader.