I wonder if there might be an error on the marriage, and her father is really Thomas Lake. He is a witness at the marriage.
In 1871 Eliza is recorded as born Turnham Green. Thomas Lake (with wife Ann and family) is living in that area - Chiswick, Middlesex in numerous census records. There is a daughter Eliza with them in 1861.
ADDED in 1851, same family in Chiswick / Hammersmith - Eliza is 6 months old.