London Fields is in Hackney and Kate and Thomas married in Edmonton so I think it is very likely that she is the Kate E Lloyd in the 1881 census below. Unfortunately her parents were James Thomas Lloyd and Elizabeth Abigail Ellwood so don't match the parents' names on her death certificate.
Name: Kate E Lloyd
Event Type: Census
Event Date: 1881
Event Place: Edmonton, Middlesex, England
Registration District: Edmonton
Residence Note: Church Road
Gender: Female
Age: 6
Marital Status: Single
Occupation: Scholar
Relationship to Head of Household: Daughter
Birth Year (Estimated): 1875
Birthplace: Hackney, Middlesex, England
Page Number: 26
Registration Number: RG11
Piece/Folio: 1388/104
Affiliate Record Type: Household
Household Role Sex Age Birthplace
James T Lloyd Head M 26 St Albans, Hertfordshire, England
Elizabeth A Lloyd Wife F 27 Redbourne, Hertfordshire, England
Kate E Lloyd Daughter F 6 Hackney, Middlesex, England
Florence M Lloyd Daughter F 4 Edmonton, Middlesex, England