My apologies for making a slight correction which should clarify your confusion about Elizabeth Lyte, daughter of Thomas Lyte of Lytescary. She was married first to Sir Richard Crane and secondly to Thomas Seymour of Bitton and Frampton Cotterell, Glos. Col. John Seymour, Royal Governor of Maryland (d. 1709) was her eldest child not her husband. In fact, she had 14 children by Seymour, all published by the Harleian Society in the Parish of Bitton records. I do not have a date of death for Elizabeth Lyte Seymour, but her youngest child, a daughter Hannah was baptized in 1666, so presumably she was still alive at that date.
In 1750 Berkeley Seymour, the senior male descendatnt of the Bitton branch was one of the claimants to the dormant Dukedom of Somerset. Among the items from _The Attorney General's Report of Edward Seymour's Claim to the Dukedom of Somerst_ was a sworn statement that lays out the Seymour descent from Edward Seymour, Lord Protector. Elizabeth Lyte is mentioned in the pedigree.
Although Berkeley Seymour clearly believed he was descended from John Seymour, bastard son of the Protector, it seems more likely that this John was a bastard son of the Protector's father instead. Berkeley believed that John the bastard was not illegitimate, but rather the son of Henry Seymour, brother of the Protector. Unfortunately as Parliament concluded the dates just didn't jive.