TV Tropes said in https://tvtropes.org/pmwiki/pmwiki.php/Main/LampshadeHanging :
Lampshade Hanging
The Order of the Stick hangs a lampshade on Lampshade Hanging with a literal lampshade.Sir Toby Belch: Is it possible? Fabian: If this were played upon a stage now, I could condemn it as an improbable fiction.
— Shakespeare, Twelfth Night, Act 3, Scene IV
Lampshade Hanging (or, more informally, "Lampshading") is the writers' trick of dealing with any element of the story that threatens the audience's Willing Suspension of Disbelief, whether a very implausible plot development, or a particularly blatant use of a trope, by calling attention to it and simply moving on.
This assures the audience that the author is aware of the implausible plot development that just happened, and that they aren't trying to slip something past the audience. It also assures the audience that the world of the story is like Real Life: what's implausible for you or me is just as implausible for these characters, and just as likely to provoke an incredulous response.
The creators are using the tactic of self-deprecatingly pointing out their own flaws themselves, thus depriving critics and opponents of their ammunition. The Turkey City Lexicon refers to this flavor of Lampshade Hanging as a "Signal from Freud", and reminds the author that if your characters are complaining about how stupid the latest plot development is, maybe your subconscious is trying to tell you something.
On the other hand, Lampshade Hanging done well can make for an entertaining piece of Medium Awareness or momentary lack of Genre Blindness. It can also be used to take care of Fridge Logic, without having to actually do anything. For this reason, it can either be seen as making a bad movie even worse or as adding clever writing and humour.
This practice is also known as "hanging a clock on it", "hanging a lantern on it", or "spotlighting it". In the film industry it's sometimes called "hanging a red flag" on something, after the screenwriting adage, "To hang a red flag on something takes the curse off of it," meaning that to lampshade something decreases the negative effects it might otherwise have. Teodolinda Barolini referred to this as "the Geryon Principle" in reference to how Dante narrates how unbelievable his "true" story is the more fantastical it gets. We went with our title because it's the one used in the Mutant Enemy bullpen.
Can also be combined with a Hand Wave, sometimes invoking an unreveal, to make explaining a plot inconsistency unnecessary. When breaking internal consistency is deliberate this trope can be used to show that, yes, it is deliberate instead of a plot hole. Can also be combined with an active attempt to avoid the trope, in which case the Lampshade Hanging turns into a Defied Trope.
Commonly seen in the self-aware shows that make up the Deconstructor Fleet; rarely used in the presence of a Drop-In Character. If large numbers of lampshades are hung, then the writers believe lampshades are Better Than a Bare Bulb, this trope's Logical Extreme.
Hypocrisy Nod and Inspiration Nod are specific types of this. Meta Guy is the fellow who does this all the time. Sometimes takes the form of This Is the Part Where.... Compare Discussed Trope, Postmodernism and Playing with a Trope. No Fourth Wall happens when characters not only discuss tropes, but the writers as well.
Not to be confused with Lampshade Wearing.
Once again, Lampshade Hanging is when attention is drawn to something that is so strange it threatens to break the Willing Suspension of Disbelief. Leaning on the Fourth Wall is for things which make sense in the story but also have a second meaning outside of the story. Try not to get these confused.(via https://tvtropes.org/pmwiki/elastic_search_result.php?new_search=true&q=lampshade+hanging&page_type=all)