Katarina's Death Lotus
As controversial as it is, this thing needs to be changed around, improved or whatever you want to do with it. I'm only suggesting this given what Season 6 is looking like for AP champions.
Death Lotus at a Glance: According to the wiki, Death Lotus is really a damage over time spell. This spell does (350/550/750 +250% AP and 375% Bonus AD) magic damage over 2.5 seconds. Death Lotus will also only target 3 enemy champions, meaning if your health bar isn't diminishing when she jumps in, then you're "safe" for now.
This actually causes a great deal of confusion when identifying Katarina as a champion. Katarina's job as of late (which is worse than her AD Counterpart, Master Yi) is to either clean up kills, or to assassinate a target, go out of control due to the amount of single target and area of effect damage, then kill the rest of the enemy team. Sadly, all of her damage has a lower soft cap, so she cannot do this anymore.
Let me explain; her ultimate damage has a soft cap, meaning that even if you were to use it all the way on one target, they would not die if they were over this soft cap. This soft cap extends to her entire combo due the fact that none of it does percent damage, and the fact that AP has an optimal soft cap on her as of this season. The soft cap is lower if they can out sustain it, out tank it, or cc/burst the crap out of her before she can do that to them. As of this season, her soft cap is probably the worse its been since even before her pre-rework stage. This is due to the fact that many MR items were buffed (for whatever reason that may be), Maw of Malmortius/Hex Drinker has become viable on a lot of new champions, Locket of the Iron Solari puts a detriment on mostly her AOE damage, but her single target damage takes a hit as well, the fact that Magic Penetration isn't as useful as it was the last 3 seasons, and because of the very nature of Katarina herself. The only way she can circumvent this is that she should hope that either:
A. She gets fed.
B. Her team composition allows her to clean up instead of being the main damage dealer.
C. The enemy team doesn't know how to deal with her well.
This causes her to be extremely feast or famine, with a relatively large disposition towards famine due to the soft cap. What's worse is her ultimate's nature. Her ultimate can do anywhere from a very small fraction of her combo damage (ultimately because it was canceled, or her targets run out of the range of her ultimate) to over 50% of her damage. That said, she's very team reliant on killing most of her targets, which is a contradiction to her role as an assassin. (NOTE: She can easily do this if any of the ABCs apply) This is two-sided; either she needs a team to prevent her from being targeted out right, and let Option B happen, or she gets someone to CC her target or enemy team, and let Option C happen. As for other assassins, I cannot say whether or not they are as reliant on their team as Katarina is.
tl;dr Katarina is crap atm and the below are suggestions to help her along.
With all that in mind, here are my suggestions for her.
The first one is very conservative and has no real affect on her numbers.
Change: Death Lotus' range is increased from 550 to 600/650?.
Katarina will prioritize enemy champions with the least amount of health.
Pros:
QoL change.
Feels like the right direction compared to everything else.
Cons:
Not very dramatic; it's a band aid to a much larger problem wound.
This next one is quite odd.
Change: When Katarina uses Death Lotus, her W gains 200 range and targets her Death Lotus targets after Death Lotus ends for whatever reason for 3 seconds.
More Extreme Change: Same, and her W gains 1.5x the damage.
Pros:
Lessens the Feast or Famine if her Ultimate gets shut down.
Cons:
Very Arbitrary.
Not enough fall back; if ultimate did nothing in the first place, neither will this.
This last one is very controversial due to how well the community deals with Percent Max Health Damage: Change: Death Lotus now does 25%/37.5%/50% percent + 2.5% per 100 AP Max Health magic damage over 2.5 seconds to all enemy champions in range. Pros: Aligns her identity as a team assassin. Tank Buster!... Cons: ...but squishies can still survive. Percent Max Health Anything is/has been extremely controversial.
tl;dr of the above: Pick your poison: Targeting Priority Ability Sync Percent Max Health Magic Damage