It sounds logical that you would perform a lavation in a lavatory, doesn't it? And it is logical: both words come from Latin lavare, meaning, appropriately, "to wash." English picked up a few other words from this root as well. In medicine, the therapeutic washing out of an organ is lavage. There is also lavabo (in Latin, literally, "I shall wash"), which in English can refer to a ceremony at Mass in which the celebrant washes his hands, to the basin used in this religious ceremony, or to other kinds of basins. Even the word lavish, via a Middle French word for a downpour of rain, comes to us from lavare.
Word History
Etymology
Middle English lavacioun, from Latin lavation-, lavatio, from lavare