The intricate dynamics of fluid interfaces, disordered liquid-liquid emulsions, and soft microfluidic droplet crystals, collectively known as soft glass materials (SGM), pose challenges to non-equilibrium thermodynamics and hold profound implications for engineering applications such as combustion, materials design, and food processing. Advances in SGM modeling within the ERC COPMAT project offer opportunities for innovative mesoscale materials in fields like tissue engineering, photonics, and catalysis. The Lightweight Lattice Boltzmann (LB) scheme, which relies on hydrodynamic moments, models SGM by preventing droplet coalescence including near-contact interactions (NCI) due to surfactants. Integrated into LBcuda, an open-source software optimized for GPUs, it efficiently simulates complex flows while saving electrical energy, in line with the goals of the European Green Deal. The LBFAST project aims to optimize LBcuda's implementation for High performance computing (HPC) clusters powered by Graphical Processing Units (GPUs), achieving processing rates of several hundred GLUPS while using only 50% of computational resources, resulting in a 75% reduction in energy costs compared to standard LB methods. This enhancement enables accelerated production rates for industrial applications and aligns with the criteria of the EuroHPC Joint Undertaking, benefiting users addressing energy and environmental challenges in the next exascale computing generation.