We used molecular dynamics simulation of a neat two-dimensional Lennard-Jones fluid to examine how the distribution of local densities found around an atom varies as the critical point is approached. Through this analysis, we discovered that mean local density enhancements arise as a necessary and direct consequence of the long-range density inhomogeneities present in such fluids, thereby establishing a relationship between the local and long-length-scale phenomena. Additionally, we uncovered a second, "potential-induced" mechanism which generates mean local density enhancements at low bulk densities. The competition between these two mechanisms of local density enhancement formation enables us to explain why these enhancements are not maximized at the critical density, as well as to explain how the location of this maximum will depend on intrinsic experimental parameters such as the size of the local region and the strength of the solute-solvent potential interaction.