The image, thanks Ancestry, of her baptism register w/birth date, transcript by me:

“                                  Fol.128
“                           Baptisms Solemnized
“In the PARISH of ST GEORGE, HANOVER SQUARE, in the COUNTY OF MIDDLESEX, in the Year 1836 May
“. . . .
“When baptized:       June 1 1836
“No:                  510
“Child’s Forename:    Georgiana Caroline
“Parents’ Forenames:  Thomas Atherton & Mary Elizabeth
“Parents’ Surname:    Powys
“Abode:               Grosr. Place
“When Born:           9 Jany. 1836
“Profession:          Lord Lilford
“Celebrant:           W.H. Dickinson
_____________________

Not found in 1861 census

In 1871 he was a Capt of yeomanry and JP, neither too strenuous and they were at Park Cottage, Upper, Brampton Brian, Knighton, Herefords:

First name(s)  Last name  Relationship  Marital status  Sex  Age  Birth year  Occupation  Birth place
John N     Fazakerley  Head  M  M  37  1834  Captain of Yeomanry. JP.  London, 18 Upper Brook St
Georgiana  Fazakerley  Wife  M  F  35  1836  -                         London, Chesterfield St
John       Whiteman    Serv  U  M  25  1846  Butler                    Warwickshire, Warwick
William    Healy       Serv  U  M  37  1834  Coachman                  Rutland, Barrowden
Isaac      Barbery     Serv  U  M  17  1854  Page                      Cornwall, Tregasky
Harriet    Reynolds    Serv  U  F  24  1847  Lady’s Maid               Ireland, Newbliss
Mary       Rowlands    Serv  M  F  47  1824  Cook                      Herefords, Ayaneshy(?)

Ref:
Archive reference  RG10
Piece number       5595
Folio              11
Page               14
Combined:          1871 ref: RG10, piece 5595, folio 11, p. 14
__________________

In 1881 they were at 2, The Lees, Folkestone Town, Elham, Kent:

First name(s)  Last name  Relationship  Marital status  Sex  Age  Birth year  Occupation  Birth place
John N       Fazakerly  Head  M  M  47  1834  Jp for rutland  London, Middlesex
Georgiana C  Fazakerly  Wife  M  F  44  1837  Peers daughter  London, Middlesex
Mary E F     Powys      SinL  S  F  39  1842  Peers daughter  London, Middlesex
Harriet      Reynolds   Serv  S  F  34  1847  Ladys maid      Ireland
Elizabeth    Grigg      Serv  S  F  48  1833  Cook            Plymouth, Devon
Annie        Philpott   Serv  S  F  21  1860  Parlour maid    Hythe, Kent
Annie        Webb       Serv  S  F  18  1863  Kitchen maid    Folkestone, Kent

Ref:
Archive reference  RG11
Piece number       1009
Folio              115
Page               35
Combined:          1881 ref: RG11, piece 1009, folio 115, p.35
____________________

In 1991 she and John were still at Folkestone with a niece (step niece almost certainly) with them instead of her sister.  This time their surname was spelled Fazakerley.
____________________

No children found in these two censuses.

No children births found with the surname of Fazakerley or Fazackerley from 1850 to 1880 and with a mother’s maiden name of Powys.

I think they dsp.
____________________

Her death index:

First name(s)       Georgina Caroline
Last name           Fazakerley
Sex                 Female
Death year          1896-1900
Place               Frankfurt
Country             Germany
Vessel              Frankfurt
Type                Consular/Overseas
Source              Gro Consular Death Indices (1849 To 1965)
Records year range  1896-1900
Archive reference   DCON
Volume              10
Page                767
Line number         21
Archive             General Register Office
Record set          British Armed Forces And Overseas Deaths And Burials
–––––––––––––––––––

Her burial at Lilford cum Wigsthorpe church:

“                      Page 27.
“BURIALS in the parish of Lilford cum Wigsthorpe in the County of Northampton in the Year 1897
“. . . .
“Margin Note:  Third daughter of Thomas Atherton III Baron Lilford died in Wisbach Germany Apr. 7 1897
“Name:         The Hon: Georgiana Caroline Fazakerley
“Abode:        73 Harrington Gardens, London.
“When buried:  April 14 [ 1897 ]
“Age:          61
“Celebrant:    F M Stopford
___________________

Again from Ancestry only, this probate index:

1897
FAZAKERLEY the honourable Georgiana Caroline of 73 Harrington-gardens Middlesex (wife of John Fazakerley esquire) died 7 April 1897 at Wiesbaden Germany.  Administration (with Will) London 1 June to the said John Nicholas Fazakerley  Effects £117156 0s. 10d.  Resworn September 1897 £114309 4s. 8d.

I would order this will if I could get at the Government web site constructively.  IT might confirm that she had no children.
___________________

Their marriage index:

First name(s)     Georgiana Caroline
Last name         Powys
Marriage quarter  2
Marriage year     1859
Marriage Finder   Georgiana Caroline Powys married one of these people
                  John Nicholass Fazakerley
District          Oundle
County            Northamptonshire
Country           England
Volume            3B
Page number       351
Record set        England & Wales Marriages 1837-2005
_________________