Nancy - The source of my information on the English Lynams was the LDS International Genealogical Index (IGI), individual search, for the British Isles.You can access this through any LDS Family History Center.My search yielded literally hundreds of Lynams/Linams, and I was overwhelmed to find it a more common name than I had assumed.Unfortunately, there is no easy way to link these English Lynams/Linams with those who came to this country.
Since I had no real starting point for my family origins, I used the most basic assumption that the family had retained the spelling of the name "Linam."Therefore, I looked only at Linams -- not Lynams.Since John & Margaret were most definitely Lynams, the Bedfordshire connection wouldn't necessarily apply.My family were also slave-owners, which Quakers abhorred, so I believe John & Margaret were probably unrelated.Somewhere in my research I believe it says that John was from Derbyshire, and I believe he was born @1640.If his brother Thomas was within 10 years in age, I would estimate that the children would have been born between 1650 and 1680.Using this hypothesis, I looked in the IGI data:
I found no Thomas Lynam born between 1650 & 1680, but I did find a Thomas Lynam (possibly the father), b. 1626, c. Oct 1626 in North Wingfield, Derby, England.His father was John Lynam and mother Alice Allin.
Next I looked for Elizabeth Lynams b. 1650-1680.There were two:Elizabeth, b. @1653 in St. Kew, Cornwall, and Elisabeth, c. 1662, in Thimbleby, Lincolnshire.None in Derbyshire, plus the parents' names don't include a Thomas.
Sorry, I know this is not encouraging.John & Margaret seem to be a dead end, since they apparently had no children.Anders Loinam, on the other hand, had many descendants.If Anders was indeed Swedish, however, I don't see any direct connection to John & Margaret.
Hope this is helpful in some way.Happy to correspond with you further to clear up any loose ends.Best regards, Jim