Stability assessment of a lossy power system during a transient is challenging because of the stringent time limit for a conclusion to reliably support protection functions. A coverage-based stability assessment is pursued with focus on resolving computation and scalability issues. This approach involves online tracking of each generator's electromechanical state using a local quasi-steady-state sinusoidal measurement model, and determining whether the state is enclosed in an offline-computed post-fault region of attraction (RoA) at the time the RoA is established by a protection action. The RoA is numerically estimated offline with a scalable ellipsoidal expansion algorithm, and the need for the expansion is delineated. The approach to transient stability assessment is tested on a lossy 68-bus system subject to transmission faults. The study concludes that the coverage-based stability assessment can offer significant advantages in both reliability and swiftness over the existing assessment methods.