O-RAN systems in virtualized platforms (O-Cloud) offer performance boosts but also raise energy concerns. This paper assesses O-Cloud's energy costs and proposes energy-efficient policies for base station (BS) data loads and transport block (TB) sizes. These policies balance energy savings and performance fairly across servers and users. To handle the unknown and time-varying parameters affecting the policies, we develop a novel online learning framework with fairness guarantees that apply to the entire operation horizon of the system (long-term fairness).