Proto-Indo-European *sleiH- "bluish" became Serbo-Croatian šljìva "plum" and šljivovica "plum brandy", borrowed as slivovitz. *sleiH- also became Old English slāh and English sloe, blackthorn fruit.
According to the AHD, *sleiH- became Latin līuēre "to be bluish" and līuidus "bluish", borrowed thru French as livid.
Lavender is from Anglo-French lavendre from medieval Latin lauendula. It was thought to be connected to lauare "to wash", either because the plant was used in perfuming baths or laid among linen. But the OED notes that "on the ground of sense-development this does not seem plausible; a word literally meaning 'washing' would hardly without change of form come to denote a non-essential adjunct to washing". Another suggestion is that lauendula is from *līuendula, from līuidus. Lavender is bluish.