I have tried and so far failed to find any mention of Eliza for the 1911 census in case it gave clues - possible record of her in a Portsmouth asylum.
You did find the right 1911 census for Eliza.
Very shortly after her husband's ship went missing, Eliza gave birth to another child, Stella May.
On this birth record, Eliza gives her full name as Eliza Lucy Alice Love. See attached.
Eliza Lucy Alice Love died in the "lunatic asylum" in 1921. See attached. She could have been seeking medical help, as she was fighting TB for years.
So this poor woman's life, in short, was losing a 4 yr old in 1893 (Lilly Lindsey), waiting "forever" in 1899 to find her husband was lost at sea followed almost immediately by giving birth to a daughter that died very soon after, losing both sons to orphanages, (and not even the same orphanage), then suffering for years with TB until it killed her.
The daughter that did remain with her on the 1901 census, Lilian Queenie Love, seems to be this one:
https://discovery.nationalarchives.gov.uk/details/r/D7431627 , in the British Women's Royal Naval Service from 1918 - 1919. If you register there, you can download it for free. There is not much on it, except she lists a friend as her next of kin. That could hint at her mom being very sick at the time.
In 1901, the oldest son, Lawrence Francis Love, was in a British Orphan Asylum in Slough, Bucks.
This site describes it :
https://www.childrenshomes.org.uk/BritishOrphan/About 2/3 of the way down on that link, it gives the object of the orphanage, and mentions that for entry, among other things, the marriage certificate of the parents must be produced, so at least you know there was a marriage!
