In 1731 he married Lady Elizabeth Lee, daughter of the 1st Earl of Lichfield.
His son Edward succeeed to the baronetcy and was later ennobled as Earl of Lichfield.
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He was the son of Patrick Crowe of Ashington, Northumberland, and brother of Christopher Crowe, diplomat, who married Charlotte, daughter of Edward Lee, 1st Earl of Lichfield, widow of Benedict Calvert, 4th Baron Baltimore.