Lawrence Leach married Elizabeth Mileham at Hurst, Berkshire on Feb 2,1605/6, who survived him. "Elizabeth Leech" was in the list of Salem church members compiled in late 1636.
They had as many as eight children: Agnes, (possibly) Clement, Robert, Henry, John, Richard, Margaret, & RACHEL Sibley GOLDTHWAIT.
Source: Anderson's Winthrop Fleet.

Elizabeth Mileham Leach Website:
https://www.familysearch.org/tree/person/details/LBP6-DRD
Reference information for year of birth and year of death
My late great grandmother Emma Julia Leach Davies was a DAR member (NSDAR #603958). Her son Col. Thomas Melville Leach Davies was a member of the Sons of the American Revolution (NSSAR #91964) They left genealogical notes suggesting the birth and death dates of Elizabeth Mileham Leach to be 1585-1674.
The sources for birth year/location and Elizabeth's father's name are below:

Web Page (Link to the Record)
http://wc.rootsweb.ancestry.com/cgi-bin/igm.cgi?op=GET&db=wrandall&id=I0894

•Name: Elizabeth Mileham
•Sex: F
•Birth: 1585 in Village of Gravesend, Parish of Gravesend (Kent) England
•Death: 1674 in Beverly Settlement (Essex) Massachusettrs Bay Colony
•Note:
MILEHAM
The name Mileham, Millam, and Milam occurs frequently in the Hurst registers, but no baptism for an Elizabeth appears there during that time period. Nevertheless, Elizabeth (Mileham) Leach was probably the daughter of John Mylam of Hurst, Plowmaker, who left a will dated 12 April 1604 (no evidence of probate), mentioning wife Elizabeth to be executrix, daughter Elizabeth, son Andrew, daughter Agnes (a minor) and a daughter Alice (also a minor). Overseers were to be "well beloved neighbors" John Coles and Thomas Johnson.

Also another source for the birth year of 1585 is below:
1585: Elizabeth Milham was born.
"Leach Family Record: descendants of Lawrence Leach of Salem, Mass., 1629, through his son Giles, on Bridgewater, Massachusetts, 1665" by Samuel Chessman; , Samuel; J. Munsell's Sons, publisher; 1898 (929.2 L467C ACPL)