TL:DR My thoughts on most of the cards and suggestions for the future, or for revising this should OP want my opinion. Long time Yugioh and League player
Several of the cards are hard to read, nearly painful to read in some instances, you need to reword things to not only be clear but enjoyable. Additionally several cards don't draw upon the theme of the champion/subject. In addition some things are absurd in power level (Which is your choice in making them but what is the point in such over powered cards that have no draw backs?) Though some cards are just terribly bad and don't reflect how awesome they could be if designed.
Major examples include Vlad having the ability to remove himself from play to dodge attacks or targeted spell/traps and being able to resummon himself in attack/defense position.
You could have done Talon a bit better and had his effect deal direct damage based on the level of the monster he destroyed, based off a card that is randomly revealed from their hand, or a set amount to fit his theme of bleeding. Or if you wanted to think of him as an assassin you could have perhaps made an equip card that could offer him a boost in attack but the real nice thing would let him dodge an attack (his ult).
For Riven unless you were going to combine mechanics/cards that switch her to attack/defense then a better idea would be to have lower attack/some defense and have her empowered during her own battle phase and her opponents. Something like 1800/1500 with a 300 point boost to attack during your attack phase, 300 defense boost during a defense.
(Also seeing every monster being 4 stars, some might benefit from having lower or higher ratings)
Morgana as a Union monster quite fits actually, her being mainly a support. Though I think that her being summoned with say 3 counters and then being able to protect herself from destruction would be cool. (Of course being able to give those counters to other monsters)
Additionally it would have been fun to see a Morgana with a binding effect, making a monster unable to switch positions for a turn.
Leblanc's early game is strong and as an assassin you don't really see them as a later game threat. Thus her having so many stars seems odd. 3 Would seem a great fit. However the effect you provide is actually really nice, loved it.
Kled was really good, not sure I could think of anything to really improve it, same with Kat.
Draven was a real let down. It doesn't really make use of how it feels to play him when you cash out. Instead of the effect you provided, it would have been better to give him say a 100 point attack boost per star-level of the monster he destroyed till the next turn. Something with perhaps counters if you wanted to make it more of a snowball effect and have him gain a counter for each kill so he ramps up into something nasty. Alternatively it would have been cool to see him with a one-time effect that he could Ult an opponents life points for a one time only 1,000 points of damage. Also why zero defense? He does have a spell that allows him some mobility.
Darius was a big disappointment. Should have made this guy 8 stars, with a solid defense and great attack. It would have allowed to show how he as a juggernaut is slow to come in, but once there is a pain to deal with. Something like 2800/2400 or maybe 3000/2200. As for the effect I think it would have been better if he had a ani-monster destruction effect, sorta fits him being an unstoppable machine. Combine it with an equip spell for his Axe that gives him a boost of attack that say lets you heal Life points for destroying a monster and you got a much better themed card.
For Cassiopeia a trigger effect where she can expend her effect to reduce the attack (or defense) of a monster by a set amount (say 500) would be cool. Or if you wanted to play with her ult she could have a defensive effect where you can stop the attack and put them into defense mode. Though depending on the strength you might want to add a discard card effect, or limit the power in how much you can do it. Additionally she should have an effect to also be a reptile-type in addition to her spell caster effect.
Walls of Citadel way to strong. I'd say if you want a long lasting attack stopper it would work. Swords of Revealing Light is similar in fashion. Opponent should be allowed to set, it's not like having walls prevents your opponent from preventing their next attack or defense.
Roar of the Slayer is a mess. I'd just turn it into a quick play that can only be played while Sion is out. Turning one or all monsters to defense position once activated.
Not sure what Sigil of Noxus is really supposed to do. Sure it can fit with some of the cards and not be a disaster, but it just feels wasted a bit. With a city based on power, something that empowers its attacks or attack points might be better. Perhaps a powerful effect while its on the field, and then a terrible effect when it leaves the field. Showing that while your on top and strong the world is yours, but once you fall no one has sympathy for your weakness. Perhaps giving a boost to attack, but banishing the monster or costing you life points.
For Noxus, I think a better fitting theme would be empowering the strongest of your monsters. Perhaps offering being untargetable by spell/trap cards while they have the highest attack total. Or perhaps instead it allows a search mechanic or recycle mechanic. Maybe like you have "Noxian" in each of the cards name (Example: Noxian - Sion, Noxian - Katarina) and having them get a small but nice power up (say 200 or 300 points) Then granting you strength when you destroy a monster in battle or say attack directly, letting you look at the top 2-3 cards of your deck and allowing you to put them on the bottom of the deck. That could count for the political shuffling of power and mind games that goes on in the city.