A high-performance polarization stabilizer is highly desirable for many fields, such as optical communication, optical remote sensing, and optical measurement systems. It should simultaneously feature high tracking speed, compact size, low insertion loss, and low cost. Here, we experimentally demonstrate an integrated polarization stabilizer based on thin-film lithium niobate (TFLN) photonics and look-up table (LUT) method. Our device consists of two components, serving for measuring and manipulating polarization states, respectively. Our device can achieve a polarization measurement accuracy of lower than 0.6°. For polarization stabilization, TFLN photonics enables low-voltages, fast-response, and low-loss operations, and the LUT method enables convergence with one loop cycle. Therefore, our device can achieve a tracking speed of up to 100 Krad/s with low-speed analogy-to-digital and digital-to-analogy conversions.