Have you considered that you may have wrongly attributed this - Elizabeth Ann Fitzgerald was baptised 25 Apr 1914 at St Luke, Stepney Tower Hamlets London - to the Fitzgerald/Tyler union, given their marriage date, the fact that the other two children were born in the 1920s and you say no sign of Elizabeth after birth.
I think she belongs to Fitzgerald/Saunders and that it is they who were living at the Poplar address you have indicated.
Their second son was registered at Poplar:
FITZGERALD, HENRY CHARLES mmn SAUNDERS
GRO Reference: 1908 J Quarter in MILE END OLD TOWN Volume 01C Page 428
FITZGERALD, THOMAS GEORGE mmn SAUNDERS
GRO Reference: 1912 J Quarter in POPLAR Volume 01C Page 958
The births then in 1910 and 1914 are probable:
FITZGERALD, MAUD ALICE mmn SAUNDERS
GRO Reference: 1910 D Quarter in STEPNEY Volume 01C Page 330
FITZGERALD, ELIZABETH ANN mmn SAUNDERS
GRO Reference: 1914 J Quarter in POPLAR Volume 01C Page 972
I doubt that the chap married to Tyler is the same in both cases. Guess he could have married two Alice Maud’s, though. 😉
Jamjar