In practical computational fluid dynamics (CFD) applications related to high Reynolds numbers, large-eddy simulation with wall modeling (WMLES) is widely adopted to alleviate the prohibitive near-wall resolution requirement of wall-resolved LES~\cite{Bose2018}. The lattice Boltzmann method (LBM), owing to its simple algorithmic structure and excellent parallel scalability, provides an attractive alternative to traditional Navier-Stokes solvers for turbulent flow simulation. A wall model for lattice Boltzmann-based LES that combines Newton-Raphson iteration with the analytical Musker wall function has been developed to impose a target wall shear stress~\cite{Malaspinas2014}. This approach enables the reconstruction of near-wall velocity profiles with very coarse grids while preserving accuracy. The method demonstrated robust performance in turbulent channel flows at a friction Reynolds number of up to $O(10^6)$, achieving accurate predictions of mean profiles with 10 uniformly distributed grid points across the channel half-height. Building on the validated Newton-Raphson wall model, we investigated two alternative ways to evaluate wall stress. First, a precomputed look-up table replaces the iterative wall law and allows us to compute $u_{\tau}$ without solving an equation. Second, a neural network trained on DNS data predicts $u_{\tau}$ directly from the flow at the first off-wall node. These implementations allow us to quantify and compare performance across the Newton-Raphson, look-up table, and neural-network approaches for GPU-based WM-LES. In the meantime, the neural-network model provides a flexible framework that will be extended in future work to more general wall-modeling scenarios where the Newton-Raphson approach can encounter converge issues, e.g., flows with strong pressure gradients.