Lu Sui (路隨 or 路隋) (776 – August 16, 835), courtesy name Nanshi (南式), was an official of the Chinese Tang Dynasty, serving as a chancellor during the reign of Emperor Wenzong.
Lu Sui was born in 776, during the reign of Emperor Daizong. His ancestors were originally from Yangping (陽平, in modern Hanzhong, Shanxi). His great-great-grandfather Lu Jie (路節) served on staff of Li Zhen the Prince of Yue (an elder brother of Emperor Daizong's great-great-grandfather Emperor Gaozong); his great-grandfather Lu Weishu (路惟恕) served as a prefectural prefect; and his grandfather Lu Junzhi (路俊之) served on the staff of a crown prince.
Lu Sui's father Lu Mi (路泌) was known for being learned and studious. When, during the revolt of the general Zhu Ci against Emperor Daizong's son Emperor Dezong, Emperor Dezong was forced to flee the capital Chang'an, first to Fengtian (奉天, in modern Xianyang, Shaanxi) and then to Xingyuan (興元, in modern Hanzhong), Lu Mi followed the emperor in his flight, leaving his wife and children at Chang'an. During flight, he was also injured when stricken by an arrow. He eventually came to serve under the important imperial general Hun Jian and was much respected by Hun, and he participated in Hun's campaign against another rebel general, Li Huaiguang, as Hun's secretary. He was with Hun in 787 when Hun met with the Tufan prime minister Shang Jiezan (尚結贊) to sign a peace treaty — when Shang laid a trap for Hun, intending to capture Hun; Hun escape, but many of his staff members were captured or killed. Lu Mi was captured and taken to the Tufan capital Lhasa. It was said that in his years at Lhasa, Lu Mi became well-learned in Buddhism, and was much respected by Tufan's king, but was never allowed to return to Tang until his death.