We develop a 3D Lattice Boltzmann Method (LBM) with Large Eddy Simulation (LES), and a wall model, to simulate interactions of fully turbulent flows with ocean structures. The LBM is based on a hybrid method, combining inviscid (far-field) and viscous (near-field) perturbation flows. The inviscid flow is solved with potential flow theory. The near-field perturbation flow, which satisfies perturbation Navier- Stokes (NS) equations, is solved with a novel perturbation LBM model (pLBM), based on a collision operator using perturbation equilibrium distribution functions (DFs). The pLBM, previously applied to direct NS modeling (DNS) is extended to highly turbulent flows using a LES, and a wall model representing viscous/turbulent sub-layer near solid boundaries. The pLBM is first validated for turbulent channel flows, for moderate to large Reynolds numbers, Re in [3.7 x 10^4; 1.2 x 10^6], and we find the modeled plate friction coefficient and near-field turbulence properties agree well with both experiments and DNS results. We then simulate the flow past a NACA-0012 foil using both a regular LBM-LES and the pLBM-LES models, for Re = 1.44 X 10^6. A good agreement with experiments and results of other numerical methods is found for the computed lift and drag forces, and pressure distribution on the foil. The pLBM results are either nearly identical or slightly improved, relative to LBM results, but are obtained with a significantly smaller computational domain and hence computing cost, thus demonstrating the benefits of the new hybrid approach.