I found Lettice's baptism record showing she was born on 13 January 1836 to William Lloyd and Anne Lewis in Llangendeirne.
On her baptism father William occupation farmer
Lettice Lloyd
Birth Date   13 Jan 1836   Llangendeirne, Carmarthenshire, Wales
Baptism 20 Mar 1836 Abergwilly, Carmarthenshire, Wales
Denomination   Calvinistic Methodist
Father   Wm Lloyd Mother    Anne Lewis
I can’t find a marriage to  David Harris  

 Nor can I find the family on 1861 census - Perhaps they didn’t marry ? 
Is this Lettice on 1851 census?
Lettice Lloyd Age 16 born   Llangendeirne, Carmarthenshire, Wales, servant
Civil Parish or Township   Llandefeilog
Town   Scyborfawr Carmarthenshire
Sub-registration district   Llangendeirne
Piece   2472
Folio   305
Page number   14
Have you seen this 1881 census entry could this be Lettice with her mother ?
Lettuce Davies Age   45  born   Llangendeirne, Carmarthenshire, Wales
Civil parish   Llanelly
Street Address   28 Panteg Row
Condition as to marriage   Married
Piece   5375
Folio   92
Page number   7
Household Members 
David Davies 48 Head occ  Railway (Ry Lab)
Ann Lloyd 79 Mother in Law Llandyfeilog, Carmarthenshire
Looks as if they married 1860
Letitia Lloyd age 21
Marriage 26 Oct 1860 St Trinity Church Felinfoel Llanelly
Father William Lloyd , farmerSpouse David Davies 21 cc block layer father Daniel, gardener
Both made their mark, abode Felinfoel