When sheared suspensions are simulated, Lees-Edwards boundary conditions allow more realistic computational setups as they remove the need of a domain bounded by shearing walls (as in Couette-type flow) which bias typical flow structures. Lees-Edwards boundary conditions therefore allow investigation of pure bulk properties in a quasi-infinite system. In addition, they improve the computational efficiency of the simulations as the whole domain can be used to calculate averages. We propose an implementation of Lees-Edwards boundary conditions for lattice Boltzmann simulations of particulate suspensions, combined with an accurate treatment of fluid-particle interactions. The algorithm is validated using a simple single-particle benchmark and further applied to a fully resolved suspension flow. Shear-thickening behavior, which is prolonged to higher shear rates as compared to Couette flow results, could be observed.