Demacia and Noxus do both hold a specific degree of popularity when it comes to champions, with a good 10+ champions belonging to either location. Geographically speaking, we have no clue where on earth Demacia is, but from Gragas' (old) lore, it placed Noxus somewhere just south of the Freljord. However, Gragas' lore has changed, and the mention of Noxus' location has been changed/removed as well. Though, back before the Freljord update, Gragas' lore was kind of stupid, being that he became the swollen beast that he is by drinking booze irradiated by a Noxian nexus.
Demacia is heralded as the paragon of justice and glory, with what can be assumed to be gold and silver spires lined with bright blue banners and pennants. We can also guess that the leaders have been known to be eccentric, with Jarvan III rescuing Xin Zhao from the Noxian gauntlet, and Jarvan IV gaining Shyvana as a companion of the court - leading even the bold and faithful soldiers of the Demacian military to be curious about their decisions. We also have knowledge, albeit small, that Demacia isn't an invulnerable bastion of faith, and even monsters or assassins can lurk within its walls. We have Shauna Vayne's lore to tell us this, as it's her reason to become the Night Hunter. But, their military requires a degree of prestige, which allows Quinn and her companion Valor to take their place as a revered scouting team. They also seem to be okay taking a yordle diplomat (
) and her shadow (
) into their fold, although for the reason of Poppy's bravery in bringing Jarvan his crown, and Galio being created by a Demacian in the first place. We can also glean from certain items (
) that Demacia has a distinct knack for ornamental items that boast defense, and wings are prominent designs. Especially winged swords. Demacians friggin' love winged swords.
Noxus, however, is more colorful than Demacia. Mostly red, but that's a better color than Demacia. Their political system is one based on strength and the ability to fight - albeit it seems to allow strategically superb cripples into higher ranks, in the case of Jericho Swain. Where Garen would be the epitome of Demacian virtue and strength, Darius, the Hand of Noxus is the epitome of Demacian strength and cruelty. (reflected in his lore when he kills a turncoat to raise morale, and reflected in-game with the hidden buff where getting a kill on a champion with Noxian Guillotine sends all nearby minions, ally and enemy, fleeing in fear.) A vanguard commander who instills fear and respect into all who witness him; that is the type of soldier Noxus brings to the table. Some, though, think that the emphasis on fear is pointless and excessive. This is the point of Riven's self-imposed exile, after seeing Singed decimate an Ionian town and Noxus' own forces with his demented poison. Noxus is above nothing in the pursuit of power, whether it's making a twisted noxious machine out of an old executioner (
), or turning an unyielding terror into an unliving abomination (
). The latter was, as we know, only possible because of an ancient and largely unknown coven hiding beneath the streets of Noxus; the Black Rose. But, even with the considerate lawlessness of the city's powers that be, the city itself has laws that citizens must abide. Murder is one thing that they're against, possibly only on the Noxian-to-Noxian level, which is evidenced by Vladimir's flight from Noxus after killing his friends. And, one could see why, as the penalty would be a death show engineered by the Glorious Executioner, Draven. While normally, executions in Noxus were gauntlets of large swathes of criminals or captives pitted against each other 'til the last man succumbed to his wounds, Draven often took the stand and gave the crowd an honest show, Whirling Death and glinting axes abound in spatters of blood. What more could a Noxian want? ...A bedside ambassador, would be the answer. Cassiopiea du Couteau. Daughter of the High General of Noxus, and ambassador of the city. Her original lore placed her as a seductress who stole secrets from other ambassadors, telling her father how to cripple and weaken his enemies before war begun, but she was turned into a serpent by a Freljordian oathblade. In the current lore, she hired Sivir, who was also once the Battle Mistress of Noxus, but now simply a mercenary, to guide her through a Shuriman tomb. After planting a knife in her back and trying to steal the legacy of the Ascended, she was transformed into the serpentine creature she is now by a great statue. What of her sister and sibling-of-honor? Katarina was raised as an assassin, though this is likely to provide duality to Cassiopiea's role as an informant. And they both share a technical "sibling" - Talon, the Blade's Shadow. He swore himself to the High General's service in exchange for his life, and he seems to honor only him; bladework is all that matters to the ruthless assassin. And, recall earlier how it's stated that they're above nothing when it comes to the advancement of cruel warfare? Singed and Warwick are testament to that. Singed's mad, psychotic concoctions being tested on live humans, and himself, to the point that his flesh is marred and needed to be covered by bandages, as well as Warwick's ceaseless hunting for test subjects through supernatural methods. And, like above, we can guess from specific items (
) that they express extreme dislike for stuff not sharpened. Even their armor must have sharp bitz.
...That actually kind of tired me to write up, but...That's as much of Noxus' and Demacia's lore as I can gather from the lore and items I know of champions from either location. I hope this served well!