It appears two families have been mashed together. I don't find the 1635 marriage record of Thomas Lawton and Elizabeth Salisbury, but it seems plausible.
It appears, however, that John Salisbury and Margaret Crowley are a different family -- from Denbighshire in Wales, not Cranfield in Bedfordshire. They are the parents of William Salisbury, the immigrant, who is from Denbighshire. On Geni John Salisbury is said to be from Cranfield but he is the son of a man from Denbighshire by his wife (a Tudor cousin). Not only that, John Salisbury is shown as the full brother of another John Salibsury, a member of Parliament, who is a generation older but just happened to also die in 1612.
FamilySearch appears to have indexed the Cranfield parish registers. The only Salisbury there is an Ann Salusburie who married Hen Eves in 1633. However, there are many Lawtons. George and Thomas Lawton are fathers of children born in the early 1600s. There is no baptism record for Elizabeth Salisbury and no marriage record for Thomas Lawton and Elizabeth Salisbury.
There is a baptism record 17 April 1614 at Cranfield for Thomas Lawton, son of George. This is the Thomas Lawton who married Elizabeth Elizabeth. It's striking that her birth date, (which is reported by Shurtleff as about 1614) ends up matching her husband's, but she is older by exactly two years (as she would need to be to be a daughter of a man who died in Wales in 1612).
I think this is enough to show that Elizabeth Salisbury should be disconnected from this set of parents, and her birth date changed to "about 1614". I suspect that John Salisbury and Margaret Crowley, parents of immigrant William, should also be researched with the idea that they probably did not live at Cranfield, and that John Salisbury was probably not the full brother of John the member of Parliament.
Erica, if you agree I'll leave the cleanup to you. There are curator notes and overview texts that need to be changed. Too much for me to figure out what you have there and how to change it all.