3-1-0 Katarina is dumpstering 80% of my Ahri's health without ult/passive, this is okay?

I'm 1-1-1 Ahri against 3-1-0 Katarina. I killed her solo in lane once, then Jarvan ulted and killed me under my tower while I was recalling. All three of her kills were from my team mates overstaying at low health and not responding to back pings.

I'm rushing Abyssal as first item and it is doing literally nothing to stop her from dumpstering me with Q off of minion wave -> Shunpo to me -> Auto -> Preparation -> Pick up dagger from Q using MS -> Shunpo to me -> Q -> Gunblade -> Pick up dagger from Preparation -> Shunpo. At this point, I'm at about 20% health, and none of her dagger pick ups hit me. She doesn't even bother ulting, she just backs off because she knows I'm going to charm her if she tries, and I already have to leave the lane.

Because I'm rushing Abyssal, I don't have the damage to kill her without all three R's hitting her, which isn't possible to do without dying. If I don't disengage and recall, she'll pick up the dagger from her second Q and the next Shunpo will kill me.

How the fuck is this okay? There is literally no way for me to out-play this or build against it, because Abyssal isn't stopping it. It's ridiculous that lanes against assassins become an unwinnable clusterfuck when they have a small advantage.