Vitali spaces are a simultaneous generalization of Riesz spaces, Boolean rings, MV-algebras. We study uniformities on Vitali spaces which make lattice operations, partial sum and subtraction uniformly continuous, proving that every such uniformity is generated by its 0-neighbourhood system. This result is not true in general for lattice uniformities on lattices. As consequence we obtain general decomposition theorems for exhaustive and locally exhaustive group-valued measures and decompositions of Lebesgue and Hewitt-Yosida type.