Vertical axis tidal turbines are devices that extract the kinetic energy from tidal currents. Tidal currents can be highly turbulent. Since ambient turbulence affects the turbine hydrodynamic, it is critical to understand its influence in order to optimize tidal farms. Actuator Line Model (ALM) combined with Large Eddy Simulation (LES) is a promising way to comprehend this phenomenon. In this article, an ALM was implemented into a Lattice Boltzmann Method (LBM) LES solver. This implementation gives good results for predicting the wake of a vertical axis tidal turbine placed into a turbulent boundary layer. The validated numerical configuration was then used to compute the wake of a real size ducted vertical axis tidal turbine. Several upstream turbulence rates were simulated. It was found that the shape of the wake is strongly influenced by the ambient turbulence. The cost-to-precision ratio of ALM-LBM-LES compared to fully resolved LBM-LES makes it a promising way of modeling tidal farms.