apparently, in plumbing, “lavatory” specifically means the sink

I don’t think so? Wiktionary confirms lavatory can mean (among other things) a sink or a toilet, or the room containing them. Coming from a UK newspaper I think it is safe to assume they do mean the actual toilet in this case. (edit: here is the article the tweet is about)

And as a result of checking that, I’ve now arrived at this page: https://en.wiktionary.org/wiki/Thesaurus:toilet