Edward wase going to a church in Braintree, England where new thoughts were being preached. The leaders of the church in England were not happy with the new thoughts considering it heresy. This small group of Puritans, under the direction of Rev. Thomas Hooker, wanted to leave to a place of religious freedom.
In June, Edward boarded the ship Lyon for the New World and arrived in Boston, Massachusetts Colony in good health, September 16, 1632. He settled in Newtown, several miles away.
The Rev. Hooker's group were not happy with their allotment in Newtown and so decided to move to the west. This was a difficult overland trek of about a hundred miles, driving cattle which would supply milk for their nourishment. and provide stock for the new town.
The group ended up in present day Hartford. Edward continued to prosper in this area. About 1644, he married Mary _____ and they had children, seven to be exact.
His life abruptly ended in June of 1676. He was across the Podunk River where he had property when he was attacked and murdered by Native Americans during King Philip's war (also known as Metacom's rebellion).
between 1608 and 1613 • England
Various accounts estimate his birth:
Robert Charles Anderson in The Great Migration begins puts the date between 1608 and 1613.  By about 1613 based on grants of land at Cambridge and as early as 1608 if he was sixty years old when relieved of watching and warding and training.
Conflicted birth report: about 1604, probably at Quinton near Northampton 
Conflicted birth report: No record of his birth and parentage has yet been found, but he probably was born about 1610. 
The Lyon leaves London, 22 June 1632, with Edward among the passengers 
It's Sunday evening, 16 September 1632, the Lyon set anchor in Boston Harbor, all the passengers arrived safely 
1655 Commissioner to end small causes at Northampton 
2 September 1669 Hartford coroner's jury on body of Thomas Napp. 
Edward Elmer died before 6 June 1676. He is said to have been killed by Indians east of the river at Podunk, now South Windsor, Connecticut. 
Hartford, Connecticut Colony. This would be in Hartford, Hartford, Connecticut, USA today. (Source needed)
[O]n 7 June 1676, ‘An inventory [was] taken of the estate of Edward Elmer deceased being at Hartford,’ … At the end of the Hartford inventory was a list of those ‘concerned in the estate’: ‘widow Ellmar; John Elmar aged about 30 years; Samewell Elmar aged about 27; Edward Ellmar aged about 22; Mary Ellmar aged about 18 years; Sarah Ellmar aged about 12 years." 
Edward is confirmed through Y-chromosome DNA testing. Robert Elmore and Esco Elmer match on 36 out of 37 markers (see FTDNA kits 364027 and 369990) thereby confirming their direct paternal lines back to their MRCA Edward Elmer.
Big Y and YSEQ testing of descendants of Edward's sons Edward and Samuel have shown that men on this Y line carry SNPs R-A2276, R-A2278, R-A2280, R-A2281 and R-A2283 as family level SNPs.
Text from page 637: William W. Johnson claimed in 1899 that Edward Elmer was from Braintree, Essex, England [Elmer-Elmore Genealogy. Records of the Descendants of Edward Elmer ... (North Greenfield, Wisconsin 1899), p. 5]; this is certainly possible given his presence on the Lyon in 1632, but there is no direct evidence for this proposed origin. Banks suggested that Elmer was from St. Mary Bow, London, citing only "Banks Mss." [ Topo Dict 109].
Barbour, Lucius Barnes, Families of Early Hartford, Connecticut, Genealogical Publishing Co. Inc.; Baltimore; 1982.
Text from page 235: Edward Elmer died 1676 mar Mary who m Timothy Catlin. Early member 1 Ch. Moved to Northampton. Name on Founders Monument.
John m Rosamond Ginivare
Samuel bp Mch 21, 1646 (HTR)
Elizabeth bp July 15, 1649 (HTR) died before her father m Joseph Edwards
Edward b 1654 m/1 Rebecca m/2
Joseph b 1656 (Northmptn) died July 1659
Mary b 1658 “ m Joseph Garrett
Sarah b 1664 (E Windsor) m Thomas Long
Cambridge; came in the “Lion” arriving Sept 16, 1632 with Talcott, Goodwin, Olmsted and others; one of the origina; proprietors of Hartford; his home lot in 1639 was on the east side of Main Street next north of John Talcott. Chosen chimney viewer 1651; removed to Northampton about 1656; went from there to Windsor on the east side of the river; freed from watching and warding March 5, 1667-8; killed by Indians in King Phillip's War in 1676 leaving a widow Mary. Inv. L471-15-3.
Vol. 10, page 139: Edward Elmer, the ancestor, was born in England, and died in June, 1676. He came in the ship "Lion" to Boston, Massachusetts, in 1632, and was in Hartford, Connecticut, in 1636. He was also a first settler in Northampton in 1654, and returned again to Hartford in 1660. He had a large tract of land east of the river at Podunk, now South Windsor, where he was killed by Indians in June, 1676, during King Phillip's War. His marriage probably took place in Hartford, and the Christian name of his wife was Mary.
Text from page 75, “The properties originally held by Edward Elmer, the Widow Muzzey, William Westwood, George Steele, and James and Nicholas Olmstead at the lower end of Wigwam Neck, in all about eleven acres, were gradually assembled into the ownership of the Coolidges, Mannings, and President Appleton during a century, and later to the possession of William Winthrop and Samuel Manning at the time of the Revolution.”
Text from page 78, ”The next piece of land, eight acres in area, was allotted to Samuel Greenhill, who soon transferred it to Simon Crosby. Once more a plot of three acres, Edward Elmer's, brings us just about to Bond Street on Garden Street and opposite Brewster Street on Sparks.”
J. Gardner Bartlett, The English Ancestral Homes Of The Founders Of Cambridge, Volume: 14, Pages: 79-103, Years: 1919, Copyright: 1926, Publishers: Cambridge Historical Society.
Text from page 81, “A company of about fifty families from Essex and Hertfordshire, followers of Rev. Thomas Hooker and known as the Braintree Company, many of whom came in the ship Lion in the summer of 1632, a year in advance of their leader, and most of whom removed with him to Hartford, Conn., in 1635.”
Text from page 91: Of the rest of Hooker's company who first located at Cambridge, there remain to mention Jeremy Adams, John Arnold, John Barnard, John Benjamin, Richard and William Butler, Joseph Easton, Edward Elmer, Nathaniel Ely, Richard Goodman, Stephen Hart, John Hopkins, William Kelsey, William Lewis, Richard Lord, William Manning, John Maynard, Abraham Morrill, John Pratt, Nathaniel Richards, Thomas Scott, Edward Stebbing, George Stocking, Richard Webb, and William Westwood. The exact English home of none of these has been made public to my knowledge; but we can be quite sure that practically all of them came from County Essex.
James Savage, The History of New England from 1630 to 1649 by John Winthrop, Esq. First Governour of the Colony of the Massachusetts Bay.'. Three volumes. Originally published Boston, 1853. Reprinted for Clearfield Company, Inc. by Genealogical Publishing Co., Inc.; 1996.
Volume 1, Page 107: 16 [September 1632], being the Lord's day.] In the evening Mr. Peirce, in the ship Lyon, arrived, and came to an anchor before Boston. He brought one hundred and twenty-three passengers, whereof fifty children, all in health; and lost not one person by the way, save his carpenter, who fell overboard as he was caulking a port. They had been twelve weeks aboard, and eight weeks from Land's End. He had five days of east wind and thick fog, so as he was forced to come, all that time, by the lead; and the first land he made was Cape Ann.
Edward Elmer, immigrant ancestor, was born in England about 1604, probably at Quinton near Northampton, one of the sons of Edward and Elizabeth Elmer. He came to America in the ship "Lion," reaching Boston, September 16, 1632, settled first at Cambridge and went to Hartford with Rev. Mr. Hooker's company in 1636, where he was an original proprietor, his home lot being on the east side of Main street, next north of that of J. Talcott. He was chimney viewer in 1651 and in 1654 became one of the first settlers at Northampton, one of the first board of magistrates, and chosen recorder in 1656, was a witness to a deed, from the Indians to Major Pynchon of land, comprising the town of Hadley in 1658. He returned to Hartford in 1660, and in addition to his lands there, acquired a tract of five hundred and fifty acres on the east side of the Great river in what is now the town of South Windsor which he and his sons cultivated until he was killed there by Indians in June, 1676, during King Philip 's war. He was "freed from watching and warding in 1667 and in 1669 was the only freeman of that name in Windsor. He married Mary -, probably about 1644-45, who is said to have married (second) Thomas Catlin, of Hartford. Children of Edward and Mary Elmer : John, born 1646; Samuel, baptized March 21, 1646-47; Elizabeth, baptized July 15, 1649; Edward, born 1654; Joseph, 1656; Mary, 1658; Sarah, 1664.
Text from page 89, “We will now take leave of Colchester, and returning over the old Roman road as far as Copford we then strike westward over the very ancient main highway running across Essex to the borough of Hertford. After traveling about fifteen miles we come to Braintree, another parent town of a namesake in Massachusetts. Braintree and Bocking, although separate adjoining parishes, form practically, although not officially, a single town. The twin parishes are located on rising ground above a small river, and lie on the site of a Roman station. The streets of the double village are narrow and winding and are lined with houses, many dating from Stuart and Tudor times. St. Michael's Church in Braintree is situated in a spacious churchyard in the center of the town, and dates from the fifteenth century, although much restored. Its square stone tower is surmounted by a very high pointed spire covered with slate and spreading out at the bottom to cover the full size of the tower, an unusual feature in English rural churches. Unluckily the registers of this parish before 1660 have long been missing; and as many early founders of New England came from here, the loss is a great misfortune to us. The church of St. Mary in Bocking, also located in a spacious churchyard shaded by large trees, is a much larger and more interesting structure of flint and stone in the later Pointed Style. The ancient registers of this church were also long missing, but a few years ago were found, although missing in parts, and what exists from 1558 to 1639 was printed by the late James J. Goodwin of Hartford, Conn.”
It may be possible to confirm family relationships with Edward by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
Y-chromosome DNA test-takers in his direct paternal line on WikiTree:
I do have something to add, but not with any real proof but here it is.
Edwards father maybe Theophilius Elmer-Aylmer 1547-1625 and was married to Mary Newce 1549-1638. Which leads to the Bishop John? As for the Bishops father I think we have John Aylmer also 1497- married to Helen Tyrell 1499-1521. Then is another John Aylmer 1450-1527 married to Helen MNU no dates. I have a Richard Aylmer 1419-1455 I think this is now Ireland and not England! I am hoping this helps somehow.
Well I am new to this all and want to thank all of you for your research. It has made my mind twist from left to right and back again. I am looking into all the data and building a tree myself and have not found anything to add here, Except Me Here! That's not true, I am over loaded. In time my friends and family we will over come and find our answers. When I am sure of myself and working this site. I will have something new to add that's for sure! Thanks for the ears and happy holidays.
About his wife, Anderson (GM, p 636) says this: "Marriage: By about 1644 Mary ____; she outlived her husband and married (2) Thomas Catlin. [WiLR (Windsor Co Land Records)] " Since Edward died about 6 Jun 1676, Mary must have married Thomas Catlin after 1676. The "1644" referred to in Pope is referring to Edward's marriage to Mary, NOT to Thomas Catlin's marriage to Mary.