Bringing all the info together.
Why go to the effort of registering a death if you didn't register the birth? I don't think this is a family issue but an issue with the records. I don't understand enough about the records to see what error might have happened. Why is Edwin on FreeBMD and not on GRO - or have I missed something on GRO?
Kate’s siblings:
Frederick Bramston Luard, born 3rd November 1861 - LUARD, FREDERICK BRAMSTON BRAMSTON - GRO Reference: 1861 D Quarter in WITHAM Volume 04A Page 278
Hugh Bixby Luard, born 13th October 1862 - LUARD, HUGH BIXBY BRAMSTON - GRO Reference: 1862 D Quarter in WITHAM Volume 04A Page 287
Alexander Trant Luard, born in 1863 - Not yet found (likely born 20 September 1863 looking at newspaper announcements - at Hatfield Peverel Vicarage)
Frank William Luard, born 15th January 1865 - Not yet found
Clara Georgina Luard, born 28th February 1866 - Not yet found
Amy Charlotte Luard, born 1867 (died in infancy) - Not yet found but death registered - LUARD, AMY CHARLOTTE 0 - GRO Reference: 1867 S Quarter in WITHAM Volume 04A Page 190 (Likely born 20 July 1867 looking at newspaper announcements - at Hatfield Peverel Vicarage. Article on 20 September (Alexander's birthday) - Sept. 18th, at Hatfield Peverel Vicarage, Amy Charlotte. the infant daughter of the Rev. Bixby G. Luard, aged two months.
Annette Jane Luard, born 29th August 1868 - LUARD, ANNETTE JANE BRAMSTON - GRO Reference: 1868 S Quarter in CHELMSFORD Volume 04A Page 202
Edwin Percy Luard, born 13th October 1869 - On FREEBMD not on GRO - Births Dec 1869 LUARD Edwin Percy Chelmsford 4a 203
Helen Lucy Luard, born 17th July 1871 - LUARD, ELLEN LUCY BRAMSTON- GRO Reference: 1871 S Quarter in CHELMSFORD Volume 04A Page 201
Katherine (Kate) Evelyn Luard, born 29th June 1872 - Not yet found
Trant Bramston Luard, born 5th November 1873 - LUARD, FRANK[transcription error?] BRAMSTON BRAMSTON GRO Reference: 1873 D Quarter in ORSETT Volume 04A Page 175
Rose Mary Luard, born 22nd April 1876 - LUARD, ROSE MARY BRAMSDON - GRO Reference: 1876 S Quarter in ORSETT Volume 04A Page 208
Margaret Annie Luard, born 10th March 1880 - LUARD, MARGARET ANNIE BRAMSTON - GRO Reference: 1880 J Quarter in ORSETT Volume 04A Page 263