In 1964, W. E. Lamb introduced a mode-coupling constant C to characterize the stability of a dual-mode laser. Considering quantum-dot semiconductor lasers, we calculate analytically C in the framework of a rate-equation model, which includes both the homogeneous broadening of the quantum-dot emission and the dot-to-dot carrier exchange due to wetting-layer-assisted lateral coupling. Although first established using fully symmetric laser parameters for both modes, this result is then extended numerically to nonsymmetric parameters and shows that C remains unchanged when the gain/losses are adjusted so that the two laser modes are brought to oscillate simultaneously. Finally, C is shown to depend on two parameters only encompassing the pumping, the gain material mainly through the homogeneous broadening and the dot-to-dot carrier exchange, and the cavity design. Above laser threshold, the analytic result predicts a stable dual-mode behavior whatever the conditions but with a margin that decreases drastically close to lasing threshold or at small beating frequencies.