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We show how a lattice Boltzmann (LB) can be spatially coupled with a finite difference (FD) scheme, each method running on a separate region, to solve a given problem. The typical situation we consider is a computational domain that is partitioned into two regions. The same spatiotemporal physical process extends over the full domain, but a different numerical method is used over each region. At the interface of the subdomains, the LB and FD must be connected so as to ensure a perfect continuity of the physical quantities. We derive the theoretical concepts, which allow us to link both methods in the case of a diffusion process, and validate them with numerical simulations on a two-dimensional domain. We also consider the case of different size grids for which the coupling has to be complemented with an interpolation procedure.