Suggestion for new items for the underperforming assassins.
This is primarily in itemization.
First I'd like to suggest changing Void staff from total Magic resist to bonus magic resist. One of the issues is that standard mages (Syndra, Lux, Ryze, ect.) are still doing equal to, or more damage than assassins per rotation while offering faster rotations which means more total damage as well as offering AOE damage which significantly boosts their wave clear, siege, and teamfight potential. This would stop standard mages from one shotting squishies and put them in a position where you choose them for their AOE damage, Superior utility, and higher DPS than assassins.
Next is the change that would set assassins apart: A new sheen item/ LichBane rework.
After using an ability, your next basic attack (on-hit) causes your champions damage to ignore 5% ( + 7% every 100 AP) Total Magic resist for 5 Seconds, This passive is initially locked and only becomes available if the champion using it has atleast 100 AP. Shred passive can not stack with multiple procs.
The item that this is attached to would be made Melee Only. This is so that the only champions that would/could use it are the assassins it's meant to be built on. Preferably I'd like it to be a Lichbane rework. This would mean there wouldn't have to be an additional item slot dedicated to this item and the assassins who are meant to use it already build lich as a core item as it is.
Ziggs who commonly uses it can get compensatory buffs to his Passive while someone like Leblanc doesn't use/need an item like this in the first place.
Next is the item would be the same for AD assassins, except, it would be made into its own sheen item with a damage component attached.
After using an ability, your next basic attack (on-hit) causes your champions damage to ignore 5% ( + 5% every 10 Lethality) Bonus armor for 5 Seconds, and deals (150% bonus AD) bonus Physical damage. Shred passive can not stack with multiple procs.
The actual stats of both the items and the passives can be changed however they need to be but the concept should stay the same.