Unfortunately Goth music is hard to refer to. Taking bands like cradle of filth, they use a lot of stuff which seems to be influenced greatly by opera and music back in the 1800s, Victorian Era. A lot of 'Gothic Lolita' clothes seem to be majorly based on victorian clothing. So if you are explaining to a person who doesn't know about gothic music, I suggest you mix:
Modern,
Victorian
Rock
and Awesome to your descriptions.
Something that bugs me about the whole 'Gothic' scene in Japan is the whole thing.
Gothic Lolita clothing is influenced mainly by victorian and goth clothing (Although I've yet to see an overcoat on a japanese person - if you know a pic, please give the link

)
They seem to mix Gothic and Emo(Wrist Cutters) together, although they are not the same.
For most goths, the definition of gothism is to love their life and hate everything except some things, mainly sadistic and adult stuff, plus the dark world (Sanguinarians, Zombies etc)
Emo's hate themselves and everything, have no actual pride or anything, which leads to self-harming. Or they want attention or to 'fit in' with the other emos.
Japan's version of goth mixes this up, very incorrectly.
Plus Japan don't give off very good goth or rock music, decent Rock comes from America and decent goth metal comes from the UK and Germany.
The only thing for me that Japan cannot beat about the west is the gothic music.
That is all.
I will stop rambling now

じゃまた