Anyone learn the 'preposition song' in school? (Native English speaker in US, hence sung to the tune of Yankee Doodle Dandy). We were told to envision a fallen log and the words used in the song described our location in relation the log.. "About, above, across, after, along, among, around, at..." And so on. I think I made my point. It is worth looking up if anyone needs it.
The way I translate that sentence is, "we live along the water." However, it implies that we live along the entire length of whatever the body of water is. I have never heard the word lungo used as a substitute for next to or beside. In other words, the Italian sentence makes no sense.
We live in Florida, so there is plenty of water to live "along." While I suppose there is nothing inherently wrong with the English translation given here , I have never heard anyone desribe living on the water in that way. We also have a summer house on a lake. But "on the water," is marked wrong, as I suppose "on the lake" would be. While "on the water" or "on the lake" might conjure up images of a house boat to a non-native English speaker, it is the way most Americans I know would describe such a nice home location. I would guess the expressions derived from "lakeside," "waterside," or similar words which dropped the endings, hence the "on" was literally a correct description.
Your answer is correct, more correct in my opinion than 'near the water', which is less definite. Personally, I would not say that I live along the water, but this is a regional thing. Context is relevant to what expression you might use, but there is no context for DL. If you live in a small place then 'on the waterfront', 'beside the water', 'along the water' all suggest that you are directly next to the water, nothing much between you and the water. If instead you live in a seaside suburb of a town then you might be a few streets back from the water and still say that you live on the waterfront. In my part of the world (Australasia) , 'waterfront' generally (but not exclusively) refers to something a little more developed/urban e.g. I live 'on the waterfront' in my city but have a holiday house 'on' the lake- which means 'beside' the lake, not floating on the lake! Does any of this make sense? It is complicated to explain.
As a test, I tried "next to" and "on" for "along," since both mean about the same as the "correct" response and are used more frequently in conversational English. Both were considered wrong. If the verb were "andiamo" I would understand. But "viviamo" implies a dwelling place, which is usually static.