This paper presents a nonlinear observer-based actuator fault diagnosis framework for a class of Lipschitz nonlinear systems in the presence of actuator faults, including both multiplicative and additive types. The proposed diagnosis algorithm leverages a nonlinear observer designed using a modified linear quadratic Riccati equation that ensures exponential convergence of the state estimation error, independent of the Lipschitz constant. A deterministic threshold-based detection mechanism is then developed to detect fault occurrences. The framework further distinguishes between multiplicative and additive faults by leveraging specific control strategies and dynamic analysis. Theoretical results are validated with rigorous stability proofs, ensuring robustness and fault isolation capabilities. This framework provides a systematic solution for fault detection, isolation, and diagnosis in complex nonlinear systems.