Quantum dots present the chemist with the opportunity to synthesize atomic-like building blocks with made-to-measure electronic properties. For the theorists this allows a study of the same Hamiltonian for a range of parameters. Hen we consider a lattice of quantum dots, where the dots can be prepared with a narrow distribution of properties but are never quite identical. This is unlike an ordered lattice of atoms or molecules. We report computations of the frequency-dependent dielectric response of a two-dimensional array of quantum dots, as a function of the distance between the dots. When the dots are not closely packed, the response is dominated by the Coulomb repulsion of electrons (of opposite spin) on a given dot. This gives rise to an insulator-metal transition as the expanded array is compressed. The interplay between the three effects, the "disorder" due to the size, shape, and environmental fluctuations of the dots, the coupling of adjacent dots, and the Coulomb repulsion are studied as functions of the lattice spacing. The computations are performed in the approximation where each dot carries one valence electron, but these electrons are fully correlated so as to fully account for the Coulomb blocking. This is possible by a diagonalization of the Hamiltonian in a many-electron basis. Comparison is made with experimental results for the dielectric response, as described in a companion to this paper.