The history books don't show if we're descended from royalty or not. They're pretty solid on the witchcraft angle, though.This morning I googled Lydia, and learned a bit more. I found that she was accused of murdering her husband's former employer, Henry Styles of Windsor. And sure enough, indicted and sentenced to hang.
28 Nov. 1654
[Indictment] Lydea Gilburt thou art here indited by that name of Lydea Gilburt that not hauing the feare of god before thy Eyes thou hast of late years or still dust giue Entertainment to Bather the greate Enemy of god and mankinde and by his helpe hast killed the Body of Henry Styles beside other witchcrafts for which according to the law of god and the Estableshed law of this Comon wealth thou deservest to Dye[Verdict] ye Party aboue mentioned is found guilty of witchcraft by ye Jury
from the Records of the Particular Court of Connecticut, 1639- [Hartford, 1928]
More information is online here, and in The Gilbert Family. Descendants of Thomas Gilbert, 1582(?)–1659 of Mt. Wollaston (Braintree), Windsor, and Wethersfield), ed. Donald Lines Jacobus [New Haven 1953]