This chart shows a "best guess" for the relationship between Elizabeth, and Lydia Crockett. For an alternative relationship, look at this chart.* You could add several other scenarios, since most of the sons of Thomas Crockett named one of their daughters Elizabeth, and the name continued to be popular throughout subsequent generations.
I prefer the one above for several reasons:
It is favored (but not proven) by Charles Candage**
The Elizabeth mentioned above had brothers named Richard, William, and Samuel - names which she chose for 3 of her sons.
Both Richard and Samuel Crockett, lived at some time in Gorham, Me; Samuel died there.
Her son Richard "when a boy, accompanied an uncle, probably a brother to his mother, to Gorham, Me." (LNE)
Look at this chart for another Crockett connection.
The part of the above chart in gray shows my line - yet another Crockett connection!
**Crockett genealogy, 1610-1988 : some descendants of Thomas and Ann Crockett of Kittery, Maine by Charles Samuel Candage