Wasn't it Joss Wheldon who coined it, while talking about Buffy The Vampire Slayer?
Nobody has claimed they named it. The article does note that is the variant that was used at Mutant Enemy, which is confirmed in DVD commentary by Jane Espenson, among others.
Goal: Clear, Concise and WittyI'm aware that Stargate SG 1 refered to it as "Hanging a Lantern" in a meta-episode. I'm certain it's a concept known in the industry but different terms are used.
Which is actually kind of interesting, since "lampshade hanging" and "hang a lantern" are similar enough that they probably came from the same root source, but different enough that it sounds like someone reinterpreted a metaphor at some point — "lampshade hanging" makes me think "this is going to be obvious, so let's cover it up with something pretty", while "hang a lantern" makes me think "people might trip over this, so we'd better point it out". Both work to describe the concept, but they sort of come at it from opposite directions.
In one of his Comics Buyer's Guide articles about the Willing Suspension of Disbelief (related to one scene in an issue of the Incredible Hulk in which he forgot to have Rick Jones be saved from an exploding Kree spaceship, so he wrote a "Rick jumped out at the last second, using the handy parachute he always carried around" ending), back in 1992, Peter David used the phrase "hanging a lampshade on it", and used it in such a way that it was clear he assumed his readers would know what it meant. He also mentions that writers also use the phrase "hang a lantern on it" to mean the same thing.
This predated Buffy by several years, and its use in the article made it clear that the phrase itself is older than the article.
Being in a Japanese-produced work is not enough of a difference to warrant its own trope.

Because if it is, I sure as heck cant find any proof.