Wind energy research heavily relies on LES tools to understand atmospheric flow physics. The coupling between the atmospheric flow, the wind turbine wakes, and the wind farm flows implies dealing with phenomena of highly spread length scales: from kilometric atmospheric eddies to metric wind turbine wake eddies. This difference in length scales results in immense simulations that require highly efficient numerical solvers using parallel computing resources. We developed a new wind turbine simulation software, waLBerla-wind, to tackle this challenge. Based on the LBM, it exploits LBM's performance and scaling properties on large-scale supercomputers. The wind turbines are modelled by actuator-lines or actuator-disks, representing the blades of a turbine by surrogate models, as a compromise between physical fidelity and computational efficiency. Wall modelling approaches allow for more realistic simulations of wind turbines in an atmospheric boundary layer. Previously, van der Laan et al. have illustrated the feasibility of simulating large wind farm clusters using RANS models. They used the Danish Energy Island, including 670 wind turbines, as an example to confirm their approach. However, using more accurate models, such as LES, remains challenging. In this article, we will demonstrate how LBM-based solvers, like waLBerla-wind, pave the way to accurate and affordable simulations of the interaction of multiple wind farms by combining efficient LBM algorithms for accurate collision operators with surrogate models for the turbines. We will present our results for the Grand Challenge on the Adastra supercomputer, including faster-than-real-time simulations for the Danish Energy Island wind farm cluster. We will also address different floating-point precisions and the influence of SIMD vectorisation. Finally, Adastra simulations, running on AMD Genoa CPUs, are compared in terms of performance with GPU configurations (NVIDIA graphics cards). These results open the door to promising applications, such as generating large databases to set up analytical or data-driven models or even envisage a digital twin of wind farms, allowing closed-loop wind farm control based on high-fidelity tools.