The original Abraham Leasure came from Switzerland. None of them came from Wales. The familiy's oral tradition may have confused who came from which country. Or, the author of the history book may have made a mistake.
My research into early Leasure/Lasher/Lazier/Lazure immigrants has found records of femilies coming from France, Germany, England, and Switzerland. One may even have come via Scotland. Most of them were Protestants fleeing France.
The book you are quoting is confusing, as most of those kinds of books were. I think the book begins by referring to Abraham2 (son of the original Abraham1), and his son Daniel.
Abraham2 married Margaret. Abe was born in 1713. Abraham2 and Margaret had: Daniel (1758);John (1760); Abraham (1763);Mary; Elizabeth (26 Aug. ca 1764); and Margaret (1768). These names sound similar to the names in the book you found. Daniel married Elizabeth Ryan about 1783. He died 9 Dec 1830. Elizabeth lived 1768-5 Sept 1840.