Suspicious set of births while looking for any marriage to "Eliza" or birth for Lillian, under "Burton"
Lilian (
https://familysearch.org/ark:/61903/1:1:J752-HQ1)
Claud Morriss (
https://familysearch.org/ark:/61903/1:1:JQHT-3F7 ) - Claude Maurice on freebmd, no obivious mariage/death
Edna May (
https://familysearch.org/ark:/61903/1:1:JSZV-8KM )
These all seem to disappear by 1901.
Lilian may have married Thomas Colbert in MA:
1930:
https://familysearch.org/ark:/61903/1:1:XQPY-1XLis this "Eliza"? As Eleanor, perhaps attached to wrong household (the wife in this one doesn't have a mother b. England)
https://familysearch.org/ark:/61903/1:1:XQPY-1X51940 the Colberts with "E Eleanor Carpenter", mother (matches the "Burton" christening with mother Eliza Eleanor)
https://familysearch.org/ark:/61903/1:1:K4NM-NCZThe closest match for "Eliza Eleanor" would be Eliza Eleanor Cunningham b. 1877 Derby.
There are also some possible related items for the kids under this name:
"Edna May Burton" b. 1899 may have died in 1900 in Dewsbury as "Edna Mary Cunningham", aged "0"
and "Claude Maurice Burton" b. 1898 similary is found in 1900 in Dewsbury as "Claud Maurice Cunningham", aged 2. (there are no births for these kids under "Cunningham").
Eliza herself seems to have had a rough life
born illegitimate to Eleanor Cunningham in Derby, 1877:
https://familysearch.org/ark:/61903/1:1:NJNG-NF2her mother may have married Ellis Stevenson soon after, but it looks as if he was widowed by 1881:
https://familysearch.org/ark:/61903/1:1:XQ9Y-Y45"Eliza E C Stevenson" here is probably our Eliza Eleanor.
She seems to have used a combination of these names in 1913 when she remarried in Boston to William Carpenter:
https://familysearch.org/ark:/61903/1:1:N46X-V2Where says "Ellis Stevenson" and "Eleanor Cunningham" are her parents, she is widow Warburton.
Why she then reverted to "Warburton" for two censuses running before going back to "Carpenter" in 1940, I don't know, maybe William went awol?