sugar from milk, 1843, from French, coined 1843 by French chemist Jean Baptiste André Dumas (1800-1884) from Latin lac (genitive lactis) "milk" (from PIE root *g(a)lag- "milk") + chemical suffix -ose (2).
It is the hypothetical source of/evidence for its existence is provided by: Latin lac (genitive lactis) "milk;" Greek gala (genitive galaktos), "milk;" Armenian dialectal kaxc' "milk." The initial "g" probably was lost in Latin by dissimilation. This and the separate root *melg-, account for words for "milk" in most of the Indo-European languages. The absence of a common word for it is considered a mystery.
standard ending in chemical names of sugars, originally simply a noun-forming suffix, taken up by French chemists mid-19c.; it has no etymological connection with sugar. It appears around the same time in two chemical names, cellulose, which would owe it to the French suffix, and glucose, where it would be a natural result from the Greek original. Flood favors origin from glucose.
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<a href="https://www.etymonline.com/word/lactose">Etymology of lactose by etymonline</a>
Harper, D. (n.d.). Etymology of lactose. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/lactose