This is a bit tentative, but I'm posting it on the grounds that even though it has a few holes, it might be the answer, and maybe there is better evidence to support it out there somewhere.
In 1901 Lizzie Johnson has an older brother Edward, aged 17, born in Croydon.
There are no births registered in Croydon of an Edward Johnson during 1883/4.
In the 1891 census there is a 7 year old Edward Johnson, born in Croydon, recorded as the grandson of Thomas and Frances Couchman in Mereworth, Kent. His parents are not present.
Frances Couchman, née Sears married Stephen Wenham in 1859, having born a child to him earlier in the year named Elizabeth Ann Wenham. Stephen died soon after the marriage, and Frances married Thomas Couchman in 1864.
Elizabeth appears with the family in 1871 in Linton, Kent with the surname Couchman. She is not with them in 1881, and I haven't been able to find her.
On 15 May 1881 Elizabeth Wenham, spinster aged 22 married Edward Johnson, bachelor aged 23. Father named Alfred. Edward was a plumber.
Elizabeth names her father Thomas Wenham (but perhaps we can excuse her not knowing the name of the father she didn't remember). Witnesses Alfred Johnson (brother or father), and Minnie Johnson (sister).
In December Q 1883 a birth of an Edward Johnson mother's mn Wenham was registered in Bromley district (which neighbours Croydon).
I can't see any further births of Johnson children with mother's mn Wenham.
In 1891 Edward Johnson snr is with his parents Alfred and Martha. He says he is married, but wife and child are not present.
I can't find Elizabeth.
I notice two trees on Ancestry show Elizabeth as having died in Croydon in 1894, but there is no record of this.
While acknowledging that there are gaps in the storyline, and that if true, it creates a whole new lot of questions, I'm suggesting that Louisa Wells may be Elizabeth Johnson née Wenham.
(Louisa's age is one question. If she is Elizabeth she is three years older than she should be in 1901, but then she is four years older than that in 1911, and those two records are definitely the same woman.)