The consensus on line seems to be as follows:
Lydia Spooner (Alden) (1747-1775) daughter of John Alden (1718-1821) and Lydia Alden (Lazell) (1722-1749).
John Alden (1718-1821) son of John Alden (1674-1730) and Hannah Alden (White) (1730-1807).
John Alden (1674-1730) son of Joseph Alden (1627-1697) and Mary Alden (Simmons) (1638-1697).
Joseph Alden (1627-1697) son of John Alden and Priscilla Mullins.
Clearly Lydia Spooner (Alden) can't be the daughter of John Alden and Priscilla Mullins, but it seems likely she is a descendant. Maybe we can put together the documentation.