Brain-computer interface (BCI) technology, particularly those based on electroencephalography (EEG), holds significant potential for controlling powered lower limb exoskeletons in rehabilitation contexts. This study introduces an EEG-based BCI system designed to decode anticipated gait direction, thereby enabling command of a self-balancing, overground exoskeleton. To evaluate the performance of the proposed system safely and effectively, we utilized a dynamic simulator (or a digital twin) of the physical exoskeleton, developed commercially for individuals with limited or no walking ability. Six healthy participants, wearing an EEG device, were instructed to initiate gait movements toward the direction indicated by on-screen arrow triggers (forward, backward, left, and right). A Convolutional Neural Network (CNN), operating on an 80%-20% Train-Test Ratio, was used to evaluate the system. The results demonstrated low error rates for the exoskeleton simulator, and an overall system accuracy of 0.75, reflecting the performance of the EEG-based BCI. Notably, the system had an average delay of 5 minutes in a real-time control setting, primarily attributed to its signal processing step.