well, i tested her a bit.
the nerf damage on lotus is ok, but the cd nerf hits just too hard. This is a thing everyone screams at riot from 2 years ago, but it seems they still dont realize that: Katarina only brings damage to the team. Lotus does a lot of damage if you land its full channel, but in most cases you only land half of the duration, either cuz you killed your target, or cuz you need to flee or to protect yourself (zhonyas), so you need 2 lotus in a single tf to get the benefit of one full lotus.
Katarina is very susceptible to shut down early levels, is not like akali that even with a very bad start still have the potential to carry the game, if kat have a bad start, its like playing a 4v5 because is very hard to recover from that bad early, and counting that kats early is the poorest of all the mid champ early games, youre making that early game even more poor and hard for every kat player to handle: less damage, higher cooldown, and no compensation. The CD nerf on her lotus feels exactly like the voracity nerf when her rework was released, that no matter what you cant lotus 2 times in a tf early and mid game.
My recomendation is to compensate her in other non damage places, give her more survivability, like making the % damage reduction on shunpo or its duration scale with ap, or making lotus dagger count as single target spells, like it was before the rework, so she can apply the full slow on a rylays to ensure more daggers into the opponents before they flee, or to spellvamp a bit with gunblade or WotA. Otherwise, keep the damage nerf, but revert the cd nerf.