Individual Details

The only place a parent for Lemuel is noted is in a county history biography - whether or not his father was Daniel seems somewhat questionable since he did not name a son Daniel. The following are the records I've found of a Daniel Sargent in Massachusetts at the right time. There weren't a lot of Daniel Sargents to be found.

AmericanAncestors.org
About Suffolk County Court of Common Pleas - Index to Cases, 1756-1776
The dockets and extended record books for the Suffolk County Court of Common Pleas for the period 1756 - 1776 are largely missing and many scholars speculate that the British took these volumes at the time of the evacuation of Boston in 1775. The volumes have never been located in Massachusetts, and repeated searches of the Public Record Office in London and the Provincial Archives of Nova Scotia and New Brunswick have failed to turn up the missing volumes.
The Suffolk County Court of Common Pleas File Papers (1692 - 1830) were "rediscovered" in 1974 languishing in the basement of the Suffolk County Court House.
This collection of Suffolk County Court of Common Pleas file papers to whick this index refers is stored at the Massachusetts Archives, Columbia Point, Boston. For information concerning use of the collection contact the Supreme Judicial Court's division of Archives and Records Preservation.
Citation Information
Suffolk County Court of Common Pleas - Index to Cases 1756-1776. (Online database. AmericanAncestors.org. New England Historic Genealogical Society, 2013.) From records compiled by the Massachusetts Supreme Judicial Court's division of Archives and Records Preservation, and held by the Massachusetts Archives.

Whether or not the following could be Lemuel's father isn't known.
A Daniel Sargent was present in Gloucester, Essex, MA according to the Sussex Court of Common Pleas:
In 1762, as a Merchant, he was plaintiff in a case against Samuel Pool. Case entered 23 Mar 1762 and decided 4 Jan 1762/3. £25 damages awarded.
Another case was against Thomas Loring Jr., entered 26 Oct 1764 and decided 1 Jan 1765 - Damages awarded £33.
A third case against John Rowe was entered 18 Nov 1766 and decided 1 Jan 1767 - £12 awarded.

This marriage would indicate that whether or not this is Lemuel's father, Dinah Jones could not have been his mother, if Lemuel was born in 1745.
Springfield MA Records to 1850
Book 2, Marriages 1728-1807
1751 The Banns of Matrimony between Daniel Seargeants of Fort Dummer and Dinah Jones of Springfield are hereby Enter'd the 20th of July 1751 notification posted on the same day as the Law Directs.
Daniel Seargeant of Fort Dumer & Dinah Jones of Springfield were joynd together in Marriage Octr 10th 1751
Springfield Third Church (Longmeadow) 1741-1782
Baptisms
Sept 13, 1761 being at Hinsdell I Baptizd Justin the Son of Daniel & Dinah Sergeant

Massachusetts Vital Records to 1850
Amesbury Births
SARGENT
Daniel, s. William & Mary, b. Apr 17, 1697

Amesbury Marriages
SARGENT
Daniel and Judeth Martain, June 3, 1731 * [intention also recorded]

Gloucester Marriages
SARGENT
Daniel and Lydia Stanwood, Jan 17, 1744* [intention also recorded]
Daniel & Mrs,. Mary Turner of Salem, int. Jan 8, 1763
Salem Marriages
SERGEANT
Daniel of Gloucester and Mrs. Mary Turner, Feb 3, 1763

Gloucenter Births
SARGENT
Daniel, s. Daniel and Mary, June 15, 1764
Daniel, s. Daniel bp. Sept 27, 1747


Colonial Soldiers & Officers in New England, 1620-1775
Daniel Serjant, Private, Expedition at Ft. Dummer. Served from 12 Feb 1748 to 29 Mar 1748 under Capt. Josiah Willard. . Served 7 Dec 1748 to 8 Jun 1750 under Capt. Josiah Willard. He served again under Capt. Willard. Served from 24 Nov 1750 to 25 Nov 1751, no place stated.
From Ft. Dummer, under Maj. Josiah Willard, from 26 Oct 1751 to 20 Feb 1752 - still a Private.
[No other Sargents were noted as serving with Willard]

A Daniel Sarjants served under Elijah Williams, no campaign listed, from 18 Aug 1755 to 21 Nov 1755. A John Sarjants was in the same unit but had gone in on 10 Jun 1855, but also discharged on 21 Nov 1755.

A Daniel Sargent in the Plaisted Regt. served in the company of Jonathan Fellows at Crown Point from 15 Sep 1755 to 27 Nov 1755. He died. A second entry seems to be for this same soldier - Daniel Shergent of Essex County, in the campaign at Crown Point, died Oct 1755. Regiment of Col. Thomas Berry, company not given.

Birth

1720

Scotland

Child

LEMUEL Sargent (1745 - 1820)