Burwell was born either in 1711 or in 1712 at Fairfield, the residence on Carter’s Creek in Gloucester County of his parents, Elizabeth Carter Burwell and her first husband,(1680–1721). His grandfathers were (d. 1710), a wealthy Gloucester County planter, and Robert “King” Carter, one of the wealthiest men in North America, who served as president of the governor’s Council. Burwell’s younger brother, , who built Carter’s Grove in James City County, was twice nominated for the Council but not appointed, and his youngest brother, , sat on the Council at the time of the American Revolution (1775–1783). In 1724 his mother remarried, to George Nicholas, a Williamsburg physician. According to the directions of his father’s will, Burwell’s guardian, King Carter, sent him to England to be educated. He attended Eton from 1722 to 1729, when at the age of seventeen he matriculated at Gonville and Caius College of Cambridge University. Burwell remained there for four years. Like many young men of his time, he did not take a degree, but he may have begun to study law in London at the Inner Temple in February 1733 a few months before he returned to Virginia after receiving news of the death of King Carter.
Burwell inherited a large amount of property from both parents’ sides of the family. The success of a series of lawsuits to settle inheritance rights to property in England and Virginia made him one of the wealthiest young men in the colony. Burwell continued to study law for a time after he returned to Virginia but evidently never practiced. During the third week of October 1736 he married Mary Willis. They had two or three sons and three daughters before she died in May 1746. His eldest son,(d. 1779), served in the Convention of 1776.
Lieutenant Governornoticed that Burwell returned to Virginia with a reserved and haughty manner that did not favorably impress his fellow colonists. Nevertheless, in 1742 Burwell was elected to the House of Burgesses from Gloucester County and named to the Committees of Privileges and Elections and of Propositions and Grievances. After serving in the short session that met from May 6 to June 19, he joined the top ranks of Virginia leadership. On February 10, 1743, King George II appointed Burwell to the governor’s Council. He took his seat on August 4, 1743, and remained a councillor until his death thirteen years later.
At the death of Thomas Lee on November 14, 1750, Burwell became the senior member of the Council, and because the governor and lieutenant governor were both out of Virginia at the time, he served as president, in effect acting governor of Virginia, until the arrival of Lieutenant Governoron November 21, 1751. No General Assembly met during Burwell’s administration, but he continued Gooch’s efforts to maintain peace with the Indians in the Ohio Valley, and he selected Joshua Fry and Peter Jefferson to prepare a new map of Virginia. Thus partly responsible for the famous Fry-Jefferson map, Burwell recognized its importance and remarked of Fry that “considering that we are yet a Country of Woods, it is surprising how he could draw so beautiful a Map of it.”
Often referred to in Virginia history as President Lewis Burwell, to distinguish him from several near-contemporaries of the same name, he was closely related to several other members of the Council. A sister married William Nelson (1711–1772), and his brother Carter Burwell married a sister of Philip Grymes. In the spring of 1751 Burwell’s ill health led him to visit one of the medicinal springs in western Virginia, and on several occasions the Council met at his Gloucester County residence, presumably because of his inability to travel to Williamsburg. After Dinwiddie took office Burwell never again attended the Council. The lieutenant governor wanted to replace him with a member who could participate, but the Burwells were so well connected among the powerful families of Virginia that he took no action. Dinwiddie identified the cause of Burwell’s incapacity as “a distemper in the Mind,” which may have resulted from a cancer or tumor. A nineteenth-century writer asserted that Burwell had injured his head in a fall from his horse while in England and that the lingering effects of the wound caused his poor health and death. Lewis Burwell died at Fairfield in Gloucester County on May 6, 1756, and was buried probably in the family cemetery there. His remains were later moved along with those of other family members to the yard of Abingdon Church.