Lionel's father, a namesake in 1712 predeceased his father Lionel Tollemache, 3rd Earl of Dysart &mdash; on the latter's death in 1727, Lionel inherited the earldom and five main estates: Ham House in Surrey, Helmingham Hall in Suffolk, Harrington and Bentley in Northamptonshire, and 20000 acres in Cheshire.