If there's a toilet and nothing else, then it's not a mosdó. But as soon as there's a washbasin too, mosdó is an appropriate name. It's also more... sophisticated to call a room like that "mosdó" instead of "vécé". I always say "Kimegyek a mosdóba" instead of "Elmegyek a vécére."
It is probably a more accurate description of "toilet plus wash basin", but mostly in English I understand "lavatory" to just be a euphemism for toilet. I understand that for many people, especially those from North America, hearing "toilet" evokes the image of an actual receptacle for human waste, but its perfectly polite in Australian ( and I dare say NZ and British) English at least, to say, "Excuse me where is the toilet" or "I just need to go to the toilet" i.e. the entire room, including basins, hand towels whatever is "the toilet". I don't think its helpful to be too restrictive here with the acceptable translations.