ELI5: How is Lee a surname for both Caucasians and Asians?

Yup.

Lee

English: topographic name for someone who lived near a meadow or a patch of arable land, Middle English lee, lea, from Old English lea, dative case (used after a preposition) of leah, which originally meant ‘wood’ or ‘glade’.English: habitational name from any of the many places named with Old English leah ‘wood’, ‘glade’, as for example Lee in Buckinghamshire, Essex, Hampshire, Kent, and Shropshire, and Lea in Cheshire, Derbyshire, Herefordshire, Lancashire, Lincolnshire, and Wiltshire.Irish: reduced Americanized form of Ó Laoidhigh ‘descendant of Laoidheach’, a personal name derived from laoidh ‘poem’, ‘song’ (originally a byname for a poet).Americanized spelling of Norwegian Li or Lie.Chinese : variant of Li 1.Chinese : variant of Li 2.Chinese : variant of Li 3.Korean: variant of Yi.

Li/Lee

Chinese : from a character meaning ‘minister’. This was part of the title of Gao Yao, a great-grandson of the legendary emperor Zhuan Xu, who became famous as a minister under the model emperors Yao and Shun in the 23rd century bc; he was the first to introduce laws for the repression of crime. His descendants adopted this part of his title as their surname. The use of this name continued for over a millennium to the twelfth century bc, down to the rule of the last king of the Shang dynasty, the despotic Zhou Xin. Li Zhi, the head of the Li clan at that time, displeased Zhou Xin and was executed, leaving the rest of the clan facing imminent disaster. They fled, and nearly starved to death, surviving only by eating a fruit called mu zi. When the characters for mu and zi are combined, they form the character for plum, pronounced Li. In token of this salvation, the clan changed their name to the current character for li ‘plum’. Li is now the most common surname in China. Among the many famous bearers are Lee Kwan Yew, prime minister of Singapore from 1959 to 1990; Lee Teng-hui, president of Taiwan from 1988; Li Peng, prime minister of China from 1988; and Bruce Lee (1941–73), movie actor.Chinese : from the name of a state of Li (in present-day Shanxi province), which existed during the Shang dynasty (1766–1122 bc). Descendants of the state’s rulers adopted the name of the state as their surname.Chinese : this character for Li is an altered form of 1 above.Norwegian: habitational name from any of numerous farmsteads named Li, from Old Norse hlíð ‘mountain slope’, ‘hillside’.

Source: Dictionary of American Family Names ©2013, Oxford University Press

Well I be dammned