Learning-Enabled High-Assurance Systems (lehas) are self-adaptive systems that contain one or more artificial intelligence (AI) components used for high-assurance applications, such as autonomous vehicles, smart grids, and healthcare systems. The recent exponential increase in AI use and high-profile incidents involving lehas has led to a spectrum of perceived benefits and risks of AI, particularly with respect to the perception and expectation of assurance of lehas. Furthermore, as we move towards decreasing human-based control in favor of computing-based control, it is necessary to consider more explicitly the role of accountability when considering whether to trust an ethics-aware lehas to take control. From a socio-technical perspective, we take accountability to capture three key objectives: i) obligation to (effectively) communicate/inform a stakeholder who has a vested interest of their conduct, including its justification; ii) liability for ones actions (e.g., legal responsibility), which may include punitive consequences; and iii) responsibility that includes explicitly specified obligations.