Hit and run Sadako - what can I do against this?

A small correction - Lethal does nothing for Nurse's Calling. Lethal only helps with aura abilities that have a fixed time that they operate for. Something like "see survivor's aura for (x) seconds when (y) condition is met." If there is no time limit attached, it doesn't do anything. I'd guess she's running the distorted photo addon which does benefit from it, but is more of a mindgame/chase ability rather than a tracking ability.

As far as how to counter this playstyle, my first recommendation is every survivor should be running distortion every time. I despise it as killer and live and breathe by it as survivor. Imo, it's the best perk in the game which is a bold statement, I know.

Next I'd say to pull a tape from the nearest TV before you heal or heal near unpowered tvs so she can't teleport to you to interrupt. Less universal but is often in my builds is a med kit with a syringe and a small charge addon. This gives me the ability to do one regular heal to a teammate or myself, then a delayed insta-heal to the same. This often has been game saving. Something like We'll Make It is also a great bit of kit to help counter sloppy since unless you have a crazy stockpile, you can't run syringes every build.

Aside from that, sprint burst is a good all around perk that when used well with some awareness makes it difficult for hit and run ambush killers. It gives you the speed you need to get away from the initial "surprise mfer!!" which is where most of the hits will come from. If you can avoid that first hit, you put the killer in the spot they don't want to be in, which is a time wasting conventional chase. Even if they commit and eventually get the hit, every second you waste of theirs is another one to three seconds of time hopefully being put to good use by your teammates.