From ancestry.com

Genealogical and Family History of the State of Connecticut: A Record of
the Achievements of Her People in the Making of a Commonwealth and the
Founding of a Nation. Volume IV

Lake

The Lake family is of ancient English origin, and in colonial days several
pioneers of this name came to New England. Captain Thomas Lake, son of Richard
Lake, of Erby, England, was born in 1615, and became deputy governor of the
New Haven Colony. He married Mary Goodyear and settled at an early date in
Boston, where he was engaged in trade, and had extensive land interests in
Maine. July 30, 1663, he deposed in Boston that he was about forty-eight
years of age, this deposition relating to Penobscot lands in Maine for
which he had paid rent to Colonel Temple. He was slain at Kennebec by the
Indians, August 16, 1676. His will, which was dated February 27, 1663,
and proved February 20, 1676, bequeathed to his sister, Lydia Goodyear;
to Samuel Shepherd, pastor at Rowley; to cousin (nephew) George Rokesby;
to Mr. John Sherman, pastor of Watertown; to Mr. Henry Frenchman; to wife
Mary and children, Stephen, Thomas and Anne. His widow died in 1705 and
bequeathed her estate to cousins, John and Richard Watts and Mary Treworthy.
The descendants of this Lake did not go to New Jersey, and the record of
the births of his children show that he had no son William.

Another Thomas Lake came to Dorchester, Massachusetts, and was admitted to
the church there, September 20, 1640, and made a freeman, June 2, 1641. He
was a proprietor and town officer, and died October 27, 1678, at the age of
eighty years. His will, which was proved November 14, 1678, bequeathed to the
church a piece of silver plate for the communion table; to his brother Henry
Lake and children; and to one of them, Thomas, in particular. This Thomas
evidently left no children. His nephew Thomas settled in Connecticut and
was probably of age in 1659, when he was called before the church. Alice,
wife of Thomas Lake, of Dorchester, died October 20, 1678, at the age of
seventy years.

John Lake, a tailor, also came to Boston, where he was admitted to the
church, December 2, 1643, and made a freeman, May 29, 1644. June 26, 1648,
he purchased land, and in 1669-70 he deposed in the administration of
Thomas Millard 's estate that he was about fifty-one years of age. His
will, dated August 3, proved August 9, 1677, bequeathed to wife Lucy;
brother-in-law, Matthew Coy (or Cowee) and his wife; to cousin (nephew), -
Lake; to cousins (nephews) John and Mary Lake, children of his brother Luke;
to Mary Saxton. James Taylor was appointed guardian of this nephew, John
Lake, October 6, 1677, and nothing further appears concerning the brother
Luke. John Lake had several children, but as they are not mentioned in the
will of the father, it is to be presumed that none survived him or left issue.

The records of New York show a Lake family as early as 1637, viz: Robert,
two Johns, and George Lake were in Dorchester county, Maryland, as early
as 1661. It is not unlikely that sons of Henry or Luke Lake may have gone
from Massachusetts to Staten Island, and thence with the tide of pioneers,
that were known to have taken this course, to New Jersey.