sejuani was abandoned by her mother and neglected by her grandmother. in warmother, she is shown on screen being physically and emotionally abused by her mother as a teen. annie’s stepmother is very hostile to her, calling her a monster, damaging her toy, and pushing her away. rell and kayn's backstories involve child experimentation resulting in death and child soldiers, respectively.
arguably if you read the descriptions some champion’s abilities count as psychological torture (fiddlesticks, malzahar) but it’s not really lingered upon.
in the annie cinematic, a woman raises a hand as if about to strike her young stepdaughter, then decides to harm her stuffed bear, pushing her away when she tries to take it back. early in the last volume of the warmother comic, a mother hits her teenage daughter, knocking her back, and verbally abuses her.
certain parts of lore may end sadly but this is an ongoing game with lore being updated occasionally, and the gameplay is generally not story relevant.
Some champions technically fight in the nude. Those being Aatrox, Anivia, Aurelion Sol, Evelynn, Fizz, Kindred, Urgot, Volibear, Yuumi, and Zyra, along with every voidborn champion. Most of these are animals though. Urgot is a cyborg and is missing the entire lower half of his body, Evelynn is a demon, Zyra is a plant, and Aatrox is made up of mortal flesh carved by blood magic.
mundo’s lore plays up violent/unstable behavior stemming from brain damage/mental illness, it’s played more as comedic but may be uncomfortable for some. jinx is aggressive and seems to have mental health issues, especially given the context of arcane. shaco, a monstrous clown being, has a skin where he is in a straightjacket. in the warmother comic, ashe’s mother quite likely has an unspecified mental illness involving mania and delusions (it’s even repeatedly commented on by other characters). she pushes the people under her command too hard and is willing to fight others to pursue her goals- she is shown as highly flawed but not without admirable characteristics. some champions may read as having ptsd/struggle with mental health due to trauma but it’s not always directly related to their willingness to fight, and the gameplay in general revolves around combat- there are over 100 characters with different personalities and backgrounds you can fight with.
arguably yes, in the annie cinematic- a young girl has a breakdown and loses control of her powers after multiple losses of family members and being blamed for something outside of her control.
in the annie cinematic, a young girl’s stuffed bear is aggressively tugged at and badly damaged. fire spreads from it when annie uses her powers. it is still cherished and kept close. in game, it transforms in a moving large bear and can be attacked, but will return to annie.
Some champions do use drugs as part of their moveset. First that comes to mind is Singed and his insanity potion, if potions do count. Both Mundo and Warwick are also constantly being pumped full of chemicals.
young champions may be killed in game (but they respawn.) irelia’s in game voice lines heavily implies that her young sibling (?) was killed. in lore, at least one young girl dies.
some gameplay abilities involve similar elements. darkin lore involves possession, and its most intensely shown in the varus comics and cinematics and with the characters kayn and rhaast. this is also a theme amongst some of the aspect champions- in lore, atreus lost control to the aspect of war, only to reclaim it later. leona and esp diana are influenced by the aspects, but it’s comparatively more downplayed.
mundo’s ban line is him calling someone a s*ssy, which some find uncomfortable. sett, a mixed race character (or at least fantasy equivalent- his mother is a vastaya) faces bigotry in his back story.