I'll nitpick, just a little. The profile gives a birth date of 16 Oct, and a birth location of Salem. The Kimball Family History claims 16 Oct as a baptismal date, which conflicts with the baptismal date of 23 Oct given by church records (your Am. Ancestors citation is the same as my #3 Lydia's - I used the free version instead of theirs for ease of general access).
However, the unsourced profile is the only thing that connects the 16/23 October baptismal date of #3 Lydia and a marriage of Lydia to Jonathan Ashby. The Kimball Fam. History does not tie the two together. Although it says that the family lived both in Salem and Marblehead, that could have been the case of any of the other Lydias, all living in the same county.
Without a source - even a published genealogy saying that Lydia, d. of Thomas and Mary, married Jonathan Ashby - I am not ready to connect them as parents to this Lydia's profile.