Karthus main here. I don't think he needs any straight buffs, just some qol changes to make him feel better to play.
Auto attacks: Only mentioning this because they're what everyone complains about first with him. Leave them alone. No touchey. If you can't cs with his q and autos and still run out of mana like a brain dead monkey you don't deserve to get it back super easily by csing with good auto attacks. It IS possible to cs well with his autos, you just need to play with him for a while and practice it a lot. No need to do anything here.
Passive: Give a visual indicator on screen when you're running out of time to ult. Anyone who plays Karthus has been in that situation where you shot an extra q off without realizing that that was the last second to ult, which often looses a team fight. Some animation or color change to Karth while he's in his passive to signal that you don't have much time would be nice.
W: Make the vision that it grants come from the entire wall, not just the ends. Scouting bushes is actually super hard if you aren't facing it dead on and aren't very familiar with how long the wall is at each and every rank, since it grows in size when you level it up.
E: Give it the singed treatment. Make the damage tic every .25 seconds rather than every second. This would make it so much smoother to use and feel much better when wave clearing, team fighting, and everything else.
R: Apply a 1% slow to the ability when it begins the channel. This will give you an assist if the target dies before your ult goes off. Don't add any damage to the start, that will only make DFT apply twice to everyone, which would be potentially applying almost 1000 damage to everyone on the enemy team collectively in late game, that would be stupid insane considering how much damage he already dishes out. Instead, give it the meaningless slow so that the fragile ego Vayne flash tumbling into the 16 hp Jhin with no way to avoid the death to Requiem doesn't make your ult a complete waste.
Does he need these? Probably not in my opinion. He has a positive win rate and performs fine when you know what you are doing with him. It would just be nice to see some of them go through and make him feel better to play. Karthus does have a shit ton of bad matchups, but I still that you can play him in almost any game and still have a good chance of doing well with him with how flexible his playstyle is. All you really need is a competent tank that can peel for you even when you throw yourself into the enemy's faces and you are in a good spot (Shen mains, I love you so much.)
active
ult just so that they can't possibly lose the teamfight
ult...
ult. He'd be bumped down a lot of notches because his ult can be crucial in.
ult... or even 
ult.
's auto over 
any day of the week
