Droplet transport driven by spatial variations of surface wettability plays a central role in lab-on-a-chip technologies and thermal management systems. However, designing wettability distributions that maximize droplet velocity or displacement remains challenging due to the nonlinear, interface-dominated nature of multiphase flows. In this work, we propose a numerical framework that combines an interface-resolved multiphase Lattice Boltzmann Method (LBM) with a gradient-based optimization strategy to determine optimal wettability distributions. Droplet dynamics are modeled in two dimensions on a flat plate with a one-dimensional wettability variation, providing a controlled and well-posed optimization setting. A single-component pseudopotential LBM is employed, where wettability effects are introduced through a spatially varying pseudo-density assigned to solid nodes, enabling a continuous representation of surface energy gradients. To efficiently compute the cost function gradient, a semi-discrete adjoint formulation of the LBM is derived following a differentiate-then-discretize approach. This adjoint-state model yields the gradient of a cost functional related to droplet velocity with respect to the wettability distribution at a computational cost independent of the number of control parameters. The adjoint-based gradients are systematically validated against finite-difference approximations. %\noindent Numerical results show that the optimization converges toward nontrivial wettability profiles that significantly enhance droplet transport. These findings demonstrate the potential of adjoint-based optimization coupled with interface-resolved multiphase solvers for the rational design of functional surfaces in microfluidic and heat transfer applications.