Words related to *g(a)lag-
late 14c., from French galaxie or directly from Late Latin galaxias "the Milky Way" as a feature in the night sky (in classical Latin via lactea or circulus lacteus), from Greek galaxias (adj.), in galaxias kyklos, literally "milky circle," from gala (genitive galaktos) "milk" (from PIE root *g(a)lag- "milk").
The technical astronomical sense in reference to the discrete stellar aggregate including the sun and all visible stars emerged by 1848. Figurative sense of "brilliant assembly of persons" is from 1580s. Milky Way is a translation of Latin via lactea.
See yonder, lo, the Galaxyë Which men clepeth the Milky Wey, For hit is whyt. [Chaucer, "House of Fame"]
Originally ours was the only one known. Astronomers began to speculate by mid-19c. that some of the spiral nebulae they could see in telescopes were actually immense and immensely distant structures the size and shape of the Milky Way. But the matter was not settled in the affirmative until the 1920s.
1660s, "process of suckling an infant," from French lactation, from Late Latin lactationem (nominative lactatio) "a suckling," noun of action from past-participle stem of lactare "to suckle," from lac (genitive lactis) "milk" (from PIE root *g(a)lag- "milk"). Meaning "process of secreting milk from the breasts" first recorded 1857. Related: Lactational.