The sensitivity of a monolithically integrated semiconductor ring laser gyro is severely limited by the high value of the lock-in threshold. In this work, we calculate the lock-in threshold using perturbation theory and coupled mode theory analysis. It is shown that gyro sensitivity is limited to an input rotation rate of 108 deg / h due to nonlinear coupling between the countertraveling modes. This coupling arises due to the backreflection of modes from moving index gratings, induced by rotation. Lock-in threshold is directly proportional to the strength of nonlinear coupling and spatial overlap of the modes' energy densities with periodic index perturbations. © 2016 Optical Society of America.