Elfen Lied comes firmly from the school of anime where any idea -- no matter how nonsensical -- flies. Case in point, the series is about new race of human mutants. All of which, for one reason or another, grew horns and a set of invisible arms. The series is ostensibly about whether these genetic divergences make the violent or not, but it's kind of a silly question given the show is filled with more over-the-top (and often needless) dismemberment than the average high school notebook.
As such choosing one "traumatic" moment from the series should be easy. That is to say, there really isn't one -- the show was such a nonstop gore and nudie-fest for its time that taking that aspect of the show too seriously is pretty hard. It's like getting all up in arms over a Mortal Kombat fatality: if you already know what you're here for, it really drills out the mystique.
We'll make an exception for one scene in particular. It comes in the back half of the series, but actually takes place many years in the past by our characters' reckoning. The flashback shows series protagonist Lucy in her formative days. Lucy is a mutant -- or "Diclonius" as the show refers to them -- which makes life pretty difficult. Mostly because those without telekinetic appendages don't treat their fellows too kindly.
After befriending a stray dog, and a treacherous elementary schooler, our heroine is held hostage by even more terrible tots.
Since for whatever reason violent anime has it in for dogs, Lucy's schoolmates proceed to murder the hapless pup right before her eyes. Just how great an impact the scene has on you likely depends on how you feel about dogs -- and children, for that matter. The moment is fairly vicious; the kids don't just kill the stray, but all-too-savagely bludgeon it to death with a nearby vase.
What truly twists one's gust about this scene isn't just the animal violence (though that's likely enough for some). It's the way Elfen Lied taps into the maliciousness of children. Not just their propensity for often unseen violence, but their emotional cruelty as well. Anime certainly isn't the first medium to tackle such a topic, but even more than a decade after Elfen Lied aired it's a rarity.
Though, again, how you feel about dogs and kids might color your interpretation. Lucy gives as good as she gets when the encounter ends with her liquefying her pre-teen tormentors.
Now that's more like the Elfen Lied seen in the rest of the series.