When you kill the dragon, you become thane. When you are thane, your housecarl moves in the house. I don't recall any stipulation of ownership being required. Could be wrong.
From what I remember from my first and second playthroughs, you'd get Lydia before you bought the house, so even when she wasnt with you, she was at the whiterun hall with the Jarl. When you actualy got the 5k gold and decided to buy the house, then she'd move to it.
I remember having Lydia with me before buying the house for sure.
When you kill the dragon, you become thane. When you are thane, your housecarl moves in the house. I don't recall any stipulation of ownership being required. Could be wrong.
Wrong indeed. She will approach you when you exit the keep in Whiterun, not move into a house you do not yet own.