I'll go over each character briefly and say what kind of theme I think they could fulfill. For all of them, I think keeping the essence of the character is number one, even if Riot decides to change a great deal.
I want to see him be a real doctor again. One of the both funny and scary things about Dr. Mundo was that he must have been pretty smart at some point, so is he still? Is he playing dumb? Anyways, he actually has a really great visual and "mad hulked out doctor" theme going, I think it could be enhanced. He has some great quotes too, I'd love to see more.
Another one that I think his core theme is actually pretty solid: daring pilot, a little old. Spruce up his appearance to be more fluffy, give him a bit more of a backstory explaining whatever airforce and why Bandle needs it, and for Void's sake give this man some more lines! Love his laugh, I think his voice is one of my favorite parts about him, hate that he only says like 2 things.
I'm sure a lot will need to be explained to put his lore in-line with the upcoming new Void stuff. He's League's premier monster, and I'd like him to remain that way. I also want him to still have his monstrous voice and have some more intelligent lines: I don't think he should be a big dumb monster, at the very least he's able to communicate and understand others and isn't just a mindless beast. I really look forward to seeing what Riot does with his design: I really like it, but his in-game model is ancient and could definitely look way more awesome.
This champ has been mired in mystery, and while Riot doesn't HAVE to reveal everything, SOME details of his origins would be appreciated. I think he would work as a demon in-line with Eve and Tahm. Crow Storm stays. He a scare crow!
Kayle's theme is definitely "righteous angel who brings justice". But I would love to see some gray area when it comes to opposing Morg: don't just do "good vs evil". Do "good of the group" vs "good of the individual" or something like that. Don't make Morg the bad guy exclusively.
Yordles I feel are all suffering and badly need a lore update, so hopefully Kennen will benefit from that either when he is updated, or before. I think he should keep his hyperactivity, his lighting ninja aesthetic/powers and his connection with the Kinkou. This is optional, but I'd love to see more relationships with the other members of the Kinkou, Akali and Shen.
I love that Kog'Maw is both repulsive and kind of cute, I think Kog mainly needs gameplay and visuals, though his background definitely needs some love. I want to hear some foreshadowing about his Daddy too!
Freddy Kruger here is, first and foremost, an entity that invades and probably kills people in their dreams. I'd love more lines about this, maybe some interactions on what kind of nightmares certain other Champs have. His general visual design is cool, I think he should look mostly like a ghost-like entity.
Players more knowledgeable and passionate than I have provided some great details for good ole Morde. His core theme is really strong, and I really enjoyed his current back story of unstoppable lich that could only be felled by his closest advisers. He MUST be an awesome suit of armor, I am anxious to see an updated visual of him
I did a whole thread on Nunu a little while back, I think his theme's focus should be a boy and his best friend Willump the Yeti. I want a lot more emphasis on their cooperation and how they are better than the sum of their parts.
Whoever wrote that wonderful bio for this guy, bravo, but I hate that the character we follow throughout--Atreus--has basically nothing to do with Pantheon. I want to feel more connection to him. While I understand he can't look exactly like a Spartan like he does now, I think Sparta is key to his visuals, so elements of it would go a long way towards making him feel like Pantheon.
One of League's biggest blank slates, I think almost anything is fair game to change for Rammus. As long as he's "derpy armored armadillo of few words" I think it can work.
I don't LOVE Skarner's newer lore, but I chalk this up to personal preference rather than the lore having any true problems. I think his design is already great, he just needs some polish. I want the lines "the Crystal Scar is Weeping" and "I miss my kind..." to remain, great lines.
I hate Shaco, I'm not even gonna trust myself to comment unbiasedly on this.
Its a shame that Spirit Guard Udyr wasn't just Udyr's VGU because I like a lot about this. Maybe he needs to be more "rustic" than his ult skin, more "Freljord" if you will, but visually its a great direction.
While I miss Volibear's old role as a Shaman of his people, I think some elements from his old lore could actually benefit his new status as demigod. Let him have a vision on top of the stormy mountain, let him see war as a necessary tool to protect his people. And please don't make the Ursine completely mindless: they can be war-faring, fine, but make them spiritual. We already have Sejuani and the Winter's Claw for true war tribe, the Ursine can be more religious or something. Set them apart.
Took longer than I wanted, but hopefully I sort of summarized the primary themes of each Champion. Obviously its mostly in my opinion, but I'd like to think this is, generally speaking, what is appealing about each Champion's fantasy. Feel free to dispute with me, I don't play all these guys super regularly.