Etymology Guess: Loo

I haven’t googled this yet to see if it’s true, but (I was going through old notes and found my thought process) I wonder if this is the etymology of “loo” for restroom:

l’eau = water (in French)
water closet = bathroom (in UK)
“loo” = bathroom

(update: It looks like the source is unknown, but there are two guesses that are similar to mine: http://www.etymonline.com/index.php?term=loo)