Robotic airships offer significant advantages in terms of safety, mobility, and extended flight times. However, their highly restrictive weight constraints pose a major challenge regarding the available computational resources to perform the required control tasks. Neuromorphic computing stands for a promising research direction for addressing such problem. By mimicking the biological process for transferring information between neurons using spikes or impulses, spiking neural networks (SNNs) allow for low power consumption and asynchronous event-driven processing. In this paper, we propose an evolved altitude controller based on an SNN for a robotic airship which relies solely on the sensory feedback provided by an airborne radar. Starting from the design of a lightweight, low-cost, open-source airship, we also present an SNN-based controller architecture, an evolutionary framework for training the network in a simulated environment, and a control strategy for ameliorating the gap with reality. The system's performance is evaluated through real-world experiments, demonstrating the advantages of our approach by comparing it with an artificial neural network and a linear controller. The results show an accurate tracking of the altitude command with an efficient control effort.