As micromixers offer the cheap and simple mixing of fluids and suspensions, they have become a key device in microfluidics. Their mixing performance can be significantly increased by periodically varying the inlet pressure, which leads to a non-static flow and improved mixing process. In this work, a micromixer with a T-junction and a meandering channel is considered. A periodic pulse function for the inlet pressure is numerically optimized with regard to frequency, amplitude and shape. Thereunto, fluid flow and adsorptive concentration are simulated three-dimensionally with a lattice Boltzmann method (LBM) in OpenLB. Its implementation is then combined with forward automatic differentiation (AD), which allows for the generic application of fast gradient-based optimization schemes. The mixing quality is shown to be increased by 21.4% in comparison to the static, passive regime. Methodically, the results confirm the suitability of the combination of LBM and AD to solve process-scale optimization problems and the improved accuracy of AD over difference quotient approaches in this context.