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Reliable forecasting of traffic flow requires efficient modeling of traffic data. Indeed, different correlations and influences arise in a dynamic traffic network, making modeling a complicated task. Existing literature has proposed many different methods to capture traffic networks' complex underlying spatial-temporal relations. However, given the heterogeneity of traffic data, consistently capturing both spatial and temporal dependencies presents a significant challenge. Also, as more and more sophisticated methods are being proposed, models are increasingly becoming memory-heavy and, thus, unsuitable for low-powered devices. To this end, we propose Spatio-Temporal Lightweight Graph GRU, namely STLGRU, a novel traffic forecasting model for predicting traffic flow accurately. Specifically, our proposed STLGRU can effectively capture dynamic local and global spatial-temporal relations of traffic networks using memory-augmented attention and gating mechanisms in a continuously synchronized manner. Moreover, instead of employing separate temporal and spatial components, we show that our memory module and gated unit can successfully learn the spatial-temporal dependencies with reduced memory usage and fewer parameters. Extensive experimental results on three real-world public traffic datasets demonstrate that our method can not only achieve state-of-the-art performance but also exhibit competitive computational efficiency. Our code is available at https://github.com/Kishor-Bhaumik/STLGRU