Binaural speech enhancement (BSE) aims to jointly improve the speech quality and intelligibility of noisy signals received by hearing devices and preserve the spatial cues of the target for natural listening. Existing methods often suffer from the compromise between noise reduction (NR) capacity and spatial cues preservation (SCP) accuracy and a high computational demand in complex acoustic scenes. In this work, we present a learning-based lightweight binaural complex convolutional network (LBCCN), which excels in NR by filtering low-frequency bands and keeping the rest. Additionally, our approach explicitly incorporates the estimation of interchannel relative acoustic transfer function to ensure the spatial cues fidelity and speech clarity. Results show that the proposed LBCCN can achieve a comparable NR performance to state-of-the-art methods under fixed-speaker conditions, but with a much lower computational cost and a certain degree of SCP capability. The reproducible code and audio examples are available at https://github.com/jywanng/LBCCN.