Apparently one of the guards in Whiterun is sweet on her. I've not taken Lydia on quests for a very long time -- she makes way too much noise. So I leave her to guard my stuff. Yet when I return to Whiterun, on several occasions I've seen a guard leaving Breezehome "Hail, Companion!", and when I've entered Breezehome, Lydia has been scampering up the ladder to sit in the chair and eat bread. What has Lydia been doing? lolz.
Maybe this is why Lydia is not marriage material?