Lucy in "Back in Black", where her sisters attempt to mold her into something she's not. "Spell It Out" also reveals that her siblings forgetting about her and not noticing her affect her far more than she let on, making the gags of her being forgotten Harsher in Hindsight. In the episode, she feels left behind by her siblings, and the reasons why are showcased. She would, however, cross into Jerkass Woobie territory when she casts a spell on them so she could have everything revolve around her out of spite, when her siblings walking over her was because they were genuinely unaware how she really felt. It was when Lucy finally communicated said feelings that she would find out that her siblings care about her after all.
In "Really Loud Music", Luna is pressured into abandoning her rock image in favor of becoming a glamorous popstar simply because the latter is more popular. She obviously didn't want to go through such a drastic change.
Annoying Plucky Comic Relief or not, you'll likely feel sorry for Luan in "No Laughing Matter" when it's revealed that she has sucha fragile ego that the bluntness of her siblings' criticism brings her to tears. It in fact affects her so much to the point where she completely retires from comedy.
Lincoln gets this treatment hard in The Loud House Movie. Let's see... he constantly lives in the shadow of all his 10 sisters, older and younger, to the point of being pushed out of their achievement picture and locked outside his father's restaurant, which they were celebrating in, despite him playing a large role in helping their achievements be possible. Then, he has a BSoD Song about how insignificant he is, strolling down the streets alone in the dark while doing so. Just when it looks like he'll finally get glory through being the Duke of Loch Loud in Scotland, Morag uses the Dragon Stone to mind control the dragon he's riding and destroy the town, framing him in the process. The people turning on him causes him to break down crying. Later, he has to witness his entire family being nearly murdered by Morag right before his eyes, and him risking his life to save them causes her to corner him over a cliff, where he nearly falls to his death alongside his baby sister. Despite that he ultimately makes peace with who he is, graciously gives the crown to Angus, and returns to Royal Woods with his family, it's still kind of upsetting that he didn't gain further spotlight than what he had beforehand (though he thankfully did get a new friend, a good reputation in Scotland, and a meeting with his royal ancestors from the 1600s). All this at the age of 11.
Bobby in "Stress Test." In the episode, the stupid aspects of his character are somewhat deconstructed because he is shown to genuinely struggle with passing his Achievement Test of Destiny. After failing the test four times, even with the help of Carlos, Rosa, and Carlota, he is reduced to Inelegant Blubbering, and he briefly crosses the Despair Event Horizon.
Lori, at times. She can be mean, rude and bossy toward her siblings, but as "Driving Miss Hazy" revealed, she mostly acts that way because she's afraid that no one in her family will need her anymore.
Luna: "I stink and I can't write a single song..."
Cranky Neighbor Mr. Grouse gets this treatment in "11 Louds a Leapin'". It's revealed that he's part of a big family and is unable to visit them on Christmas, and seeing the Louds together doesn't help.
Lori, Lynn, and Lola may be the meanest of the sisters, but they were also three of the first characters to get the flu in "One Flu Over the Loud House".
Lynn's aggressive and rough personality was caused by brutal bullying she experienced in her first year of middle school, which made her think that she has to act agressive in order to survive there, thus permanently scarring her personality. It’s more than likely that, deep down, Lynn suffers from a combination of hate for bullies, lack of self-esteem, an inability to face her fears and self-loathing.
Luan's behavior on April Fool's Day may be sociopathic beyond all reason and belief, but her My God, What Have I Done? moment towards the end of "Fool's Paradise" brings some potential sympathy into the entire situation; her family threatening to move away from Royal Woods (which later turned out to just be a prank) and neglect her is enough to genuinely bring Luan to tears and apologize for all she's done, resulting in an ultimate reconcile and retaliation from the rest of her family. When taking into account Luan's otherwise cheerful and childish personality, the fact that her monstrous streak only comes annually, and how her parents are too scared to punish her, it's fairly obvious that Luan is suffering from some degree of PTSD.
