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We consider a dense one-dimensional laser-driven Rydberg lattice gas with perfect nearest-neighbor blockade. The ground state of this system can be found analytically in certain parameter regimes even when the applied fields are inhomogeneous in space. We will use this unique feature to investigate the effect of an impurity—introduced by the local variation of the laser parameters—on the correlations of the many-body ground state. Moreover, we explore the role of a staggered laser field which alternates from site to site thereby breaking the sublattice symmetry. We demonstrate that this technique, which can be applied experimentally, reveals insights into the role of long-range interactions on the critical properties of a Rydberg gas. Our work highlights possibilities for the exploration of many-body physics in Rydberg lattice gases based on locally tunable laser fields.