Lattice Boltzmann method (LBM) is a relatively recent computational technique for fluid dynamics that derives its basis from a mesoscopic physics involving particle motion. While the approach has been studied for different types of fluid flow problems, its application to eddy-capturing simulations of building block complex turbulent flows of engineering interest has not yet received sufficient attention. In particular, there is a need to investigate its ability to compute turbulent flow involving separation and reattachment. Thus, in this work, large eddy simulation (LES) of turbulent flow over a backward facing step, a canonical benchmark problem which is characterized by complex flow features, is performed using the LBM. Multiple relaxation time formulation of the LBM is considered to maintain enhanced numerical stability in a locally refined, conservative multiblock gridding strategy, which allows efficient implementation. Dynamic procedure is used to adapt the proportionality constant in the Smagorinsky eddy viscosity subgrid scale model with the local features of the flow. With a suitable reconstruction procedure to represent inflow turbulence, computation is carried out for a Reynolds number of 5100 based on the maximum inlet velocity and step height and an expansion ratio of 1.2. It is found that various turbulence statistics, among other flow features, in both the recirculation and reattachment regions are in good agreement with direct numerical simulation and experimental data.