At risk of sending you off on a wild goose chase, I wonder if the Charlotte Louisa Davies born in Crewe is your grandmother. I took a quick look at the 1901 census index (I don't have access to the full record) and she is in Blackrod with what looks like 3 siblings the eldest William born in Wales and possibly a grandfather but no parents. Doesn't solve the mystery of the missing death record of course but as one of her daughters appears to have been called Lottie, the Charlotte bit could be right. It is not possible to arrange a funeral without a death certificate. Have you checked the local paper for a death notice or report of the funeral to find and contact the funeral directors to see what their records say. Most funeral directors have been in business for the last 40 years so it's worth a try.