Here's an odd question. Define "looks". The model? The VO? The concept of the character? For instance, a character like Aatrox. His lore is poorly written but has an interesting concept... "eternal spirit of war that sews violent conflict wherever he goes". Ok, cool idea. His voice over work is bland as shit, but the IDEA of it is fine... He's not a raging monster... he speaks of battle as if it was art. His look I LOATHE. Riot should have gone with an archtypical demon IMO. Instead he looks like the genderless lovechild of Marilyn Manson and Lady Gaga with a spikey sex-toy as a weapon (it even wobbles!), torn curtains for wings and a goofy helmet covering up his lack of a nose. His kit is bland, boring and generic as all hell too... he's budget Tryndamere. In the case of Aatrox the ONLY thing I like about him is his concept. I loathe the champ and am disappointed that the potentially cool thing in that lore of his got turned into the champ we got.
In any case, my POINT was... concept isn't really "lore". I like Tahm's concept, but I won't pretend Riot writes lore anymore. He's a wheeling, dealing devil who lures in the unwary, makes promises and then twists those promises. That concept is cool. Very "Old Scratch making deals at the crossroads". The catfish/frog thing is... different, but I like his look. I wouldn't say that's what drew me to him tho. It's his CONCEPT. The idea behind him. And it's how well they realized that concept in his kit. In truth, I wish he and Kali had mechanics to make accepting their "help" a double edged sword, like it's supposed to be... but I see why that is a bad idea from a design perspective.
The thing that draws me most to a champ is what they're about and how well they reinforce that with the champ's lore, look, VO, skills and aesthetics. I can't really limit it to one thing. For instance... I hate Corki. Corki is strong as hell, but I find him freakin' goofy and not in the fun GP "YARRRRRR, I be a PIRATE!" way. He feels like he doesn't belong in the setting. His kit is also a weird mush of things that don't synergy very well. Ok, so he's a poke champ with his R, but his Q and E are only really useful up close... and he's an adc but he mostly does magic damage so get Sorc shoes... yadda yadda. He's a mess. Add in that I dislike his design and... well... I don't play Corki. I dislike his concept, and that colors me poorly on the rest of him.