Which workhouse records have you looked at? Dartford?
Bexley Heath had a separate parish, have you looked at those records from 1873-1881 (in case of late baptisms/the Buttons having her baptised after she came to them) for any potential Edwards or even just a "Lily"?
Looking in Dartford registration bmds, the "Lily" birth that stands out as having no later trace is Lily Ellis in early 1874, but your Lily could easily have been born elsewhere, and then "Bexley Heath" was just the best guess of her foster family.