In this work we proposed a novel graph neural network architecture, namely LiCOMPGNN, that is able contextualise message passing by attending on both global and local edge information, leading accordingly to more complete representation of materials. Our portable framework facilitates the learning improved of representations for crystalline materials through a multimodal learning scheme enriched with reciprocal space information. We further propose a suite of LiCOMPGNN variants with varying complexity that can be suitably utilised depending on the complexity of problem at hand. We empirically tested performance of the proposed models on various prediction and supercell invariance tasks and demonstrated a very competitive performance against state-of-the-art methods while at the same maintaining very low trainable parameter counts. Our findings in conjunction with the simplicity and memory efficiency of the proposed model highlight the need for a paradigm shift towards more energy-sustainable machine learning practices, which is a critical direction we encourage further research in.