With the singing style she has adopted through her albums it's difficult to sing live, because it's a breathy voice, nasal, delicate and not loud, live would be lost with all the noise so I guess that's why she lipsyncs. Britney's "true" voice would be the one she used on the competition when she was a child. In '...Baby One More Time' you can see traces of this singing style but it's completely lost after 'Oops!... I Did It Again' since that breathy/nasal singing became her trademark.