Will he/she WALK all the way back to where she belongs? Or will he/she be back where she came from the second I get there?

Reason I'm asking is because I decided to ditch Lydia quite a bit up north, and after wandering by myself for about 10 mins, I found her again, walking towards whiterun at an extremely slow pace.
Don't wanna come back to whiterun in a bit and find out she still isn't there or even worse, got stomped by a giant or something while wandering on her own.

It's only a assumption but I am pretty sure it is correct because it works this way in all past modern Bethesda games:

As long as the player isn't around a NPC is safe walking through the landscape. So if you aren't near Lydia (or in a house or dungeon) while she walks home nothing should happen to her.
NPCs take their time walking through the landscape so if you fasttravel to whiterun you have maybe to wait a few days until she arrives.