Born about 1605, Ralph Assheton was the eldest son of Sir Ralph Assheton, 1st Baronet Assheton of Great Lever, and his first wife, Dorothy Bellingham, daughter of Sir James Bellingham of Levens in Westmorland. He was educated at University College, Oxford and at Gray's Inn in 1624. He was first returned to Parliament as member for Clitheroe in 1625.
By license granted on 17 April 1630 he married Lady Dorothy Tufton daughter of Nicholas Tufton Nicholas Tufton, 1st Earl of Thanet and his wife, Frances Cecil. The marriage was childless and ended with Dorothy's death on 28 January 1635.
On 3 February 1644, Ralph married Elizabeth, daughter of Sir Sapcotes Harrington of Rand, in Lincolnshire. There was a son born who died in the lifetime of his father. Ralph himself succeeded his father as Baronet Assheton of Lever on 18 October 1644. He and Elizabeth had separated by about 1648.
In 1657 he succeeded his cousin, Richard Assheton, in the Downham estate.
Ralph died in London on 30 January 1680.
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