Metal-oxide-semiconductor (MOS)-based thin-film transistors (TFTs) are gaining significant attention in the field of flexible electronics due to their desirable electrical properties, such as high field-effect mobility (μFE), lower IOFF, and excellent stability under bias stress. TFTs have widespread applications, such as printed electronics, flexible displays, smart cards, image sensors, virtual reality (VR) and augmented reality (AR), and the Internet of Things (IoT) devices. In this study, we approach using a low-temperature solution-processed hafnium zirconium oxide (HfZrOx) gate insulator (GI) to improve the performance of lanthanum zinc oxide (LaZnO) TFTs. For the optimization of HfZrO GI, HfZrO films were annealed at 200, 250, and 300 °C. The optimized HfZrO-250 °C GI-based LaZnO TFT shows the μFE of 19.06 cm2V−1s−1, threshold voltage (VTH) of 1.98 V, hysteresis voltage (VH) of 0 V, subthreshold swing (SS) of 256 mV/dec, and ION/IOFF of ~108. The flexible LaZnO TFT with HfZrO-250 °C GI exhibits negligible ΔVTH of 0.25 V under positive-bias-temperature stress (PBTS). The flexible hysteresis-free LaZnO TFTs with HfZrO-250 °C can be widely used for flexible electronics. These enhancements were attributed to the smooth surface morphology and reduced defect density achieved with the HfZrO gate insulator. Therefore, the HfZrO/LaZnO approach holds great promise for next-generation MOS TFTs for flexible electronics.