OK I see/remember the following:

There is a `=hamlet` as you have found https://www.openstreetmap.org/node/10752374968 which I believe is (almost) correctly tagged.

Then, looking at nearby `=suburb`, clearly this area does not belong to Lei Yue Mun (land), but at the same time, it also does not belong to Tiu Keng Leng. It therefore must be its own `=suburb`, indeed for addressing purposes.

Local articles which I read to discover this ancient village does use/mention Lau Shui Hang as some sort of "place name".