The rapid expansion of e-commerce has intensified last-mile delivery challenges, increasing congestion, emissions, and inefficiencies in urban logistics. To address these issues, this paper explores demand prediction for Logistics as a Service (LaaS) using deep learning techniques within the context of the Horizon 2020 GreenLog project. We investigate the use of hybrid Convolutional Neural Networks (CNN) and Long Short-Term Memory (LSTM) models to forecast parcel delivery volumes, leveraging historical delivery data from the Oxford-based company Pedal & Post. The CNN-LSTM model integrates spatial and temporal features, enabling more accurate short-term and seasonal demand predictions compared to traditional regression and smoothing methods. Experimental results indicate that deep learning methods can reduce forecasting errors to levels usable for operational planning, improving workforce allocation, cargo-bike routing, and micro-consolidation strategies. The findings highlight the potential of predictive analytics to enhance the efficiency, sustainability, and scalability of last-mile delivery systems, supporting urban policies aimed at reducing traffic, pollution, and delivery costs. Future work will focus on refining the models with larger datasets, addressing data inconsistencies, and integrating predictions into real-time decision support tools for sustainable city logistics.