The above submission to familysearch.org proposes that Elizabeth was born in Scarborough in 1685 (so aged 14-15 when she married, which is unusually young); again the reason is not known. It seems more likely to me that if she is a Richardson then this is her: Wintringham parish records (1672) Elezebeth daug: of Bartholomew Richardson of Scampston bap. June jth; the Wintringham records have no record of her marriage within the parish or of her death as a Richardson. However, an unconfirmed source cites North Grimston records of her baptism and marriage to Richard Crosby, both naming her father as John, so this appears to be the strongest candidate.
The above submission to familysearch.org also proposes that Richard was born around 1680 in Wintringham to a John Crosby, but apart from three burials in 1615, 1658 and 1803 the Wintringham records do not mention any Crosbys in the parish between the demise of the family in the sixteenth century and the birth of Richard's children in the early eighteenth century, so it is likely that Richard was born outside the parish.