Thank you to Mary Hustings for the following research.
At the bottom of a memorial to husband and wife David and Lucy Rice in Coldharbour Church Graveyard is an inscription to Edward Felix Rice.
The inscription reads
Also in the memory of Edward Felix Rice, 2nd Lieut. L.R.B.
Killed in France Feb 18th 1917 aged 24
Felix was the son of David James Rice and his wife, Elizabeth.
David and Elizabeth married at Christ Church in 1892 (two weddings: another daughter of David and Lucy married on the same day). Their address at time of 1911 census was 8 Grove Mansions, Clapham Common, which was also the address recorded in the Coldharbour burial register when David James Rice died in 1932. David James Rice and Elizabeth (who died in 1946) are buried in the plot next to their parents David and Lucy.
There is no evidence to suggest that Edward had any connections to Coldharbour, apart from the fact that his grandparents lived there. The fact that Edward joined the London Rifle Brigade further suggests that he lived in Clapham with his parents.
Edward died from his wounds in France on February 19th 1917 aged 24.