The erbium-doped lithium niobate on insulator (Er:LNOI) platform has great promise in the application of telecommunication, microwave photonics, and quantum photonics, due to its excellent electro-optic, piezo-electric, nonlinear nature, as well as the gain characteristics in the telecommunication C-band. Here, we report a single-frequency Er:LNOI integrated laser based on a dual-cavity structure. Facilitated by the Vernier effect and gain competition, the single-frequency laser can operate stably at 1531 nm wavelength with a 1484 nm pump laser. The output laser has a power of 0.31 µW, a linewidth of 1.2 MHz, and a side mode suppression ratio of 31 dB. Our work allows the direct integration of this laser source with existing LNOI components and paves the way for a fully integrated LNOI system.