I've found a number of John Lac(e)y birth records around the London area for between 1850-1855 but no definite record in Whitechapel. If we knew anything about his parents (approximately years or areas of birth) we may be able to find them on the 1851 census, as from the years you've given me for John's birth and arrival in Australia, I don't think we can expect to find him on any of the English census images.
If you have anything at all, however small it may seem, perhaps you could let me know.
Kay
Manager