Light's inverse square law: Does it require a minimum distance from the source?
As many have said, the inverse square law applies to point-sources. These are idealized light sources which are sufficiently small compared to the rest of the geometry that their size is of no importance. If a light source is larger, it is typically modeled as a collection of idealized light sources, potentially using integration. The exact definition of "sufficiently small" varies with application. The definition of a "point source" for astronomy is quite different from the definition of "point source" for a LCD projector.
There is actually a limit to this process. The inverse square law is only valid in its normal form if you are working on scales where light can be modeled purely as a wave. As you get very small, on the microscopic scales, those assumptions break down. You instead have to think about the statistical expectation of photons, which follows the statistical analogue of the inverse square law. Even smaller, and you start to enter the world of quantum mechanics, where you have to account for the actual waveforms of the objects under study.
Ignoring these corner cases, nearly all cases you find will have "sufficiently small" defined by macroscopic factors, like the sizes and locations of lenses. Its rare to find oneself in the world where the microscopic factors matter.
The inverse square law applies to point sources. For extended sources becomes accurate at distances that are large compared to the size of the source. At large distances the source looks like a point. What "large" means depend on the application. In the case of light fixtures, the Illuminating Engineering Society and other organizations have made judgments about what is large and what is not based on the use case. Is it room lighting? Is it illumination of products in a grocery store? Etc. There are published advice and tables to guide the lighting designer.
The inverse square law applies to point sources. A real emergency light is not a point source, and therefore the law appears to not apply at close distances, because any real point is at a varying distance from different parts of the emergency light.