She has her own small bedroom on the second floor. Lydia lives in Breezehome, when she is not serving as housecarl(housecarl means a bodyguard to a king in Danish). Both Jarl Balgruuf the Greater and Proventus Avenicci can be found in Dragonsreach in the Cloud District in Whiterun. The purchase off the house is handled through Proventus Avenicci.
The house is two-stories, quite small in size.To be able to obtain the house for purchase you have to complete the quest 'Bleak Falls Barrow' that is obtained by Jarl of Whiterun. It is located in Whiterun right beside of the Blacksmith named ' Warmaiden's' near the main-gate.