Brain-Computer Interfaces (BCIs) are a groundbreaking technology for interacting with external devices using brain signals. Despite advancements, electroencephalogram (EEG)-based Motor Imagery (MI) tasks face challenges like amplitude and phase variability, and complex spatial correlations, with a need for smaller model size and faster inference. This study introduces the LGL-BCI framework, employing a Geometric Deep Learning Framework for EEG processing in non-Euclidean metric spaces, particularly the Symmetric Positive Definite (SPD) Manifold space. LGL-BCI offers robust EEG data representation and captures spatial correlations. We propose an EEG channel selection solution via a feature decomposition algorithm to reduce SPD matrix dimensionality, with a lossless transformation boosting inference speed. Extensive experiments show LGL-BCI's superior accuracy and efficiency compared to current solutions, highlighting geometric deep learning's potential in MI-BCI applications. The efficiency, assessed on two public EEG datasets and two real-world EEG devices, significantly outperforms the state-of-the-art solution in accuracy ($82.54\%$ versus $62.22\%$) with fewer parameters (64.9M compared to 183.7M).

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