This study addresses the challenge of spacecraft attitude tracking under actuator faults through a two-level robust control allocation strategy. Initially, a control Lyapunov function based quadratic program (CLF-QP) is developed to formulate three-axis command control torques. Subsequently, a robust Lyapunov-based control allocation (RobLCA) algorithm redistributes these command torques to operational actuators. The RobLCA algorithm, designed as an optimization problem, aims to minimize tracking errors while accommodating actuator faults and their imprecise estimations. Notably, it integrates the deviation from virtual inputs as a Lyapunov-based constraint within its cost function, enhancing adaptability to unachievable virtual inputs. This optimization is then converted into a computationally efficient quadratic program with linear constraints. Simulation outcomes validate the efficacy of this integrated control strategy.