I'm assuming you haven't located Lavinia's baptism either. There is a baptism in BAmpton for an illegitimate child Lavinia Jane PARR, dau of Mary PARR who was born 29 Sep 1842 and baptised 12 April 1846. On the same day 12 Apr 1846, an Eliza HOOPER was also baptised, dau of Henry & Mary HOOPER - also in Bampton. By 1851, Mary PARR was described as Mary HOOPER, widow aged 29. A marriage was recorded for a Henry HOOPER to a Mary PARR 10 Sep 1843. So it appears that Lavinia was baptised a PARR but her mother had married Henry HOOPER after her birth.
Mary HOOPER (widow) then went on to marry William LEE 7 Nov 1852. So, did your Lavinia marry as an Eliza, using the surname PARR, HOOPER or LEE?