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The resolution of GPS measurements, especially in urban areas, is insufficient for identifying a vehicle's lane. In this work, we develop a deep LSTM neural network model LaNet that determines the lane vehicles are on by periodically classifying accelerometer samples collected by vehicles as they drive in real time. Our key finding is that even adjacent patches of road surfaces contain characteristics that are sufficiently unique to differentiate between lanes, i.e., roads inherently exhibit differing bumps, cracks, potholes, and surface unevenness. Cars can capture this road surface information as they drive using inexpensive, easy-to-install accelerometers that increasingly come fitted in cars and can be accessed via the CAN-bus. We collect an aggregate of 60 km driving data and synthesize more based on this that capture factors such as variable driving speed, vehicle suspensions, and accelerometer noise. Our formulated LSTM-based deep learning model, LaNet, learns lane-specific sequences of road surface events (bumps, cracks etc.) and yields 100% lane classification accuracy with 200 meters of driving data, achieving over 90% with just 100 m (correspondingly to roughly one minute of driving). We design the LaNet model to be practical for use in real-time lane classification and show with extensive experiments that LaNet yields high classification accuracy even on smooth roads, on large multi-lane roads, and on drives with frequent lane changes. Since different road surfaces have different inherent characteristics or entropy, we excavate our neural network model and discover a mechanism to easily characterize the achievable classification accuracies in a road over various driving distances by training the model just once. We present LaNet as a low-cost, easily deployable and highly accurate way to achieve fine-grained lane identification.