Hearing aids are typically equipped with multiple microphones to exploit spatial information for source localisation and speech enhancement. Especially for hearing aids, a good source localisation is important: it not only guides source separation methods but can also be used to enhance spatial cues, increasing user-awareness of important events in their surroundings. We use a state-of-the-art deep neural network (DNN) to perform binaural direction-of-arrival (DoA) estimation, where the DNN uses information from all microphones at both ears. However, hearing aids have limited bandwidth to exchange this data. Bluetooth low-energy (BLE) is emerging as an attractive option to facilitate such data exchange, with the LC3plus codec offering several bitrate and latency trade-off possibilities. In this paper, we investigate the effect of such lossy codecs on localisation accuracy. Specifically, we consider two conditions: processing at one ear vs processing at a central point, which influences the number of channels that need to be encoded. Performance is benchmarked against a baseline that allows full audio-exchange - yielding valuable insights into the usage of DNNs under lossy encoding. We also extend the Pyroomacoustics library to include hearing-device and head-related transfer functions (HD-HRTFs) to suitably train the networks. This can also benefit other researchers in the field.