Although that census says Wellington, I believe it should be Willington, as there is no Wellington in Derbyshire. Willington would probably be under Shardlow Reg district. However there are no Lucy Waters born in that period in that area. There is however a Lucy Wateret born 4th quarter of 1840 in Shardlow district. There is also a christening of a Lucy Wateret on 07 Oct 1840, parents John and Ann, in King Street Chapel, Derby.
My interest piqued by this, I searched the GRO for any children born Harwood with a mother Wateret or similar spelling, around the early 1860's and came up with a Charles Harwood, born Bolton 1863 J quarter, mother Waterhut. Charles Harwood was christened in Bolton-le-Moors, Lancashire on 23 Aug 1863, parents John Harwood and Lucy.
I therefore surmise she was born Wateret and has been misspelled all sorts of ways. She may even have shortened it to Waters to avoid this.
I hope this is helpful to you.