lime (n.1)
"chalky mineral used in making mortar," from Old English lim "sticky substance, birdlime, mortar, cement, gluten," from Proto-Germanic *leimaz (cognates: Old Saxon, Old Norse, Danish lim, Dutch lijm, German Leim "birdlime"), from PIE root *(s)lei- "slime, slimy, sticky" (cognates: Latin limus "slime, mud, mire," linere "to smear;" see slime (n.)). Lime is made by putting limestone or shells in a red heat, which burns off the carbonic acid and leaves a brittle white solid which dissolves easily in water. Hence lime-kiln (late 13c.), lime-burner (early 14c.). As a verb, c.1200, from the noun.
lime (n.2)
greenish-yellow citrus fruit, 1630s, probably via Spanish lima, from Arabic limah "citrus fruit," from Persian limun "lemon" (see lemon (n.1)). Related: Limeade (1892), with ending as in lemonade.
lime (n.3)
"linden tree," 1620s, earlier line (c.1500), from Middle English lynde (early 14c.), from Old English lind "lime tree" (see linden). Klein suggests the change of -n- to -m- probably began in compounds whose second element began in a labial (such as line-bark, line-bast). An ornamental European tree unrelated to the tree that produces the citrus fruit.