Confusion regarding lacunarity of koch curves with same fractal dimension but different orders
I think this is a conceptual issue. Your images are not fractals, they are approximations to fractals. Lacunarity is a property of the fractal curve, not of its approximation. The Koch curve has a specific lacunarity.

Your program computes a measure that is inspired by lacunarity, from a given approximation to a fractal. This measure determines what fraction of the image can be considered a hole at a given scale.

Your normalized lacunarity I hadn’t seen before. But it normalizes the curve by the value at r=1, the smallest possible scale in the image. Obviously at this scale the difference between your two images is the largest, since at a larger scale they should be identical (the difference is in the fine details). By normalizing by this value, it is expected that the ratio elsewhere, where the differences are smaller, will reverse.