A target that’s ulted by Kayle can still be CC’d, so you can still trap them until the Intervention duration wears off.
Kayle has to naturally push the lane using her Righteous Fury, so a good jungle camp will shut down a Kayle in lane easily.
Watch which build she decides to use be it AD/AP/Hybrid and build accordingly.
Start damaging another high priority target to bait her ult – if she ults them, you can quickly switch to her and kill her.
Pay attention to how many stacks of holy fervor Kayle has on you. Extended damage trades will make Kayle relatively more powerful. Also, Kayle’s E is not always on until a good amount of CDR, so zone out of farm when possible or engage when she’s melee.