The kinetic theory turbulence modeling is beneficial to consistently implement turbulence models developed in the framework of the Navier-Stokes equation into kinetic-based numerical methods, such as the lattice Boltzmann method (LBM). Nevertheless, the kinetic turbulence modeling is significant for a more fundamental reason: the filtering of the Boltzmann and Navier Stokes equations does not a priori lead to the same results; thus, investigating the commutations errors that differentiate them can provide hints about how to develop new turbulence models. A past analysis focused on porting the Smagorinsky model for large eddy simulations to the Boltzmann equation domain, allowing it to be implemented consistently in LBM. To understand why an attentive analysis is needed, one should realize that an effective viscosity model like the Smagorinsky model is not directly equivalent to its kinetic effective relaxation times model counterpart. Therefore, it is necessary to carefully adapt the hypothesis assumed for the eddy viscosity models to the effective relaxation time models. In addition, the stress tensor cannot be computed locally in a naive manner, just like in the DNS simulations. In our current research, we take further steps by analyzing all the commutation errors stemming from filtering the Boltzmann equation and trying to leverage their proprieties instead of adapting them to simple Navier-Stokes closures. Boundary conditions are also radically different in the macroscopic and mesoscopic turbulence modeling, leading to distinct difficulties and opportunities in each case. In this context, many wall models originally developed for Navier-Stokes modeling of turbulence have not been consistently adapted to kinetic methods. Further, the efficient adoption of hardware accelerators in numerical simulations has brought new algorithmic requirements. As a result, we investigate the opportunity of combining recent advancements in the LBM boundary condition developments with existing turbulence wall models by simultaneously taking care of the intrinsic difference between the kinetic and the macroscopic modeling of turbulence.