The cislunar space is a dynamically rich environment, in which the classical two-body assumption falls, and trajectories are significantly impacted by multi-body effects. Due to these considerations, trajectory optimization for cislunar applications presents major challenges due to increased computational effort, and thereby presenting a bottleneck for autonomous on-board implementations. Neural networks have been extensively proved to be excellent function approximators, even when the underlying mathematics is extremely complex. In this work, the aim is to explore the development and implementation of a simple and computationally inexpensive feedforward neural network that can serve as an on-board tool for the estimation of optimal trajectories between any two points (i.e., prescribed boundary conditions) within the cislunar space.