A lattice Boltzmann scheme simulating the dynamics of shell models of turbulence is developed. The influence of high-order kinetic modes (ghosts) on the dissipative properties of turbulence dynamics is studied. It is analytically found that when ghost fields relax on the same timescale as the hydrodynamic ones, their major effect is a net enhancement of the fluid viscosity. The bare fluid viscosity is recovered by letting ghost fields evolve on a much longer timescale. Analytical results are borne out by high-resolution numerical simulations. These simulations indicate that the hydrodynamic manifold is very robust towards large fluctuations of non-hydrodynamic fields.