early 15c., "of a bluish-leaden color," from Old French livide (13c.) and directly from Latin lividus "of a bluish color, black-and-blue," figuratively "envious, spiteful, malicious," from livere "be bluish," earlier *slivere, from PIE *sliwo-, suffixed form of root *sleiə- "bluish" (source also of Old Church Slavonic and Russian sliva "plum;" Lithuanian slyvas "plum;" Old Irish li, Welsh lliw "color, splendor," Old English sla "sloe").
Somehow it has come to be associated with "pale, colorless." The sense of "furiously angry" (1912) is from the notion of being livid with rage. Perhaps this is the key to the meaning shift. Rage makes some dark-red-faced; purple with rage is not uncommon in old novels (" 'My money! ye pirate! or I'll strangle you.' And he advanced upon him purple with rage, and shot out his long threatening arm, and brown fingers working in the air.") while it makes others go pale, also a figure in old novels ("At this juncture, the door opened, and, pale with rage, her eyes flashing fire, Lady Audley stood before them.")