Elizabeth St John

Not a known parent of Sarah Gregory

Matthew Saint John (b. 1588) (supposedly) married about 1610, Nottingham, Nottinghamshire, England to Elizabeth (b. 1592)

https://www.wikitree.com/wiki/St_John-181

No evidence has been found to support the existence of a family called St John in Nottinghamshire in the early 1600s. Not one baptism, marriage or burial with that surname in the online registers available at FindMyPast, FamilySearch and Ancestry.

It does not seem that John St John & Lucy Hungerford had a daughter Elizabeth St John as she is not listed in the very thorough MI for them. Three children who died young as well as those who survived to adulthood are included, even those from Lucy's second marriage.

"Heere lieth the body of Sir John St John, Knight who maried Lucy daughter & co heire of Sir Walter Hungerford of Farley, Knight by whom he had issue Walter that died young Sir John St John Knight & Baronet, Oliver that died young Katherine Anne Jane Elinor Barbara Lucy & Martha that died a child. He deceased the 20 of September 1594. She was secondly maried to Sir Anthony Hungerford Knight by whom she had Edward Bridget and Jane & then died the 4 of June 1598 This was erected by Sir John St John Knight & Baronet in the year of our Lord 1615 the 20 of Jul"

References

1. https://itsallinthesynapse.net/reports/Web%20Cards/wc01_345.htm
2. Resembles Matthias St. John Who married Elizabeth St. John