Not to me. The lavatory is the loo itself or the room that contains the toilet. It’s not the bathroom because a bathroom (in the UK) has a bath in it 
Divided by a common language, indeed…
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Yes, I can second that usage. But calling a basin a lavatory? Excuse me while my head explodes.
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Recently a plumber replaced the tap in the rental bathroom’s sink. When I saw the box he arrived with I thought he had the wrong product because the box said ‘bath faucet set’
Baffling 
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Some people have cash to burn and deserve a proper faucet marketed especially for them :). I have had a few clients who just want the “best” (=the most expensive) even if it is completely ridiculous.
Wall-mounted and faucets with electronic controls are also more expensive.
I too want a tap I can talk to, dammit!
Ho, slave! Run me a bath!
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Nope, that usage is not familiar to this British person! Ha!
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Although, thinking about the etymology of the word, it does makes sense.
I’m american and have never heard “lavatory” referring to the sink before. Only a room with a toilet.
Interesting. If you think about the word roots lavatory means a place for washing, referring to the wash basin or link, not the toilet or bathtub. Maybe it’s a more archaic term? But definitely widely used. Google lavatory and see what images come up.
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Ooops, I just saw this comment and said the same thing.
Yes, my reaction was based on usage, not etymology. I’ve heard that word in use (though probably mostly in British usage) for 30 years. One just gets used to words being used a certain way.
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It’s the term used by the architectural, design professions. It helps differentiate between a sink in the kitchen and a lav in the bathroom when writing up specs on a project. Used in the plumbing contracting biz too.
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Each sort of spigot has an inward valve that controls the stream of water through the gush. The valve quality, with or without a washer, decides the unwavering quality and toughness of the fixture. The best decisions are fixtures with strong metal, metal based metal or erosion safe workings.
The single spigot taps are commonly called “mixer” taps, safer as the hot is mixed with cold, fewer scalds. The hole in the basin or lavbo is a smaller diameter than a sink. We call the unit that the basin/labvbo sits in a vanity cabinet.