This paper reports the numerical demonstration of a silicon (Si)-compatible continuous wave laser based on the erbium-doped lithium niobate-on-insulator rib waveguide, emitting around 1531 nm by optical pumping at 980 nm. The model involves a full vector finite-element-method-based modal analysis of the proposed device with the solution of laser rate equations and propagation equations using in-house developed computer codes. Optimization of the laser cavity, which maximizes the laser output, is investigated for different values of background loss along with a set of realistic input parameters. For 0.027-dB  /  cm loss, a maximum laser output of 79.64 mW with a threshold of 10 mW is computed when 200-mW pump power is coupled to the cavity and the cavity length is optimized to 13.54 cm. For a 6.04-cm long optimized cavity, the laser threshold is reduced to 5 mW with a computed output power of 43.59 mW. The computed slope efficiencies at 20 mW of the coupled pump are 37.72% and 43.79%, respectively, for 13.54- and 6.04-cm long laser cavities. These results indicate the possibility of realizing an efficient hybrid Si laser operating at the third telecommunication window, which may find potential application in Si photonics.