Brain--computer interfaces are groundbreaking technology whereby brain signals are used to control external devices. Despite some advances in recent years, electroencephalogram (EEG)-based motor-imagery tasks face challenges, such as amplitude and phase variability and complex spatial correlations, with a need for smaller models and faster inference. In this study, we develop a prototype, called the Lightweight Geometric Learning Brain--Computer Interface (LGL-BCI), which uses our customized geometric deep learning architecture for swift model inference without sacrificing accuracy. LGL-BCI contains an EEG channel selection module via a feature decomposition algorithm to reduce the dimensionality of a symmetric positive definite matrix, providing adaptiveness among the continuously changing EEG signal. Meanwhile, a built-in lossless transformation helps boost the inference speed. The performance of our solution was evaluated using two real-world EEG devices and two public EEG datasets. LGL-BCI demonstrated significant improvements, achieving an accuracy of 82.54% compared to 62.22% for the state-of-the-art approach. Furthermore, LGL-BCI uses fewer parameters (64.9K vs. 183.7K), highlighting its computational efficiency. These findings underscore both the superior accuracy and computational efficiency of LGL-BCI, demonstrating the feasibility and robustness of geometric deep learning in motor-imagery brain--computer interface applications.