Hamilton was the son of John Lowry (1720-1781) and Martha Rogers. (?-1781). Note: his mother is called Ann in the document below in regards to the Ship Clyde.
This family was originally from Ireland.

Siblings:
David (1754-1837)
John (1760-1843
Michael (1762-1844)* married Susannah Moorhead
Hamilton (Captain) (1763-1864)*
James (??-d. 1801)
Robert Rogers (~1765-d.1812)*
Samuel (1770-1819)

Hamilton married Agnes ?? (1770-1825). She passed away before Hamilton immigrated from Ireland to Canada with his children in 1826. (See son Hamilton's marriage record.)

Children of Cpt Hamilton Lowry and Agnes: (memorials found are marked with an *)
Michael Lowry 1782 (in question) came a year before family. ( also, might be a nephew)
*Osay (Lowry), b.1792; married John Moorhead (came a year later at age 17)
*Nancy Agnes (Lowry), b.1794; married William Maxwell
George Lowry, b.1796
Robert Lowry, b.1798
*Margaret Lowry, b. 1799; married a Gabey (a.k.a Mary?)
*Savage Lowry, b 1802; had 8 children with Ann Jane.
Samuel Lowry, b. 1804
*James (Lowry) Lowary, b.1806
*Hamilton (b. 1809-1865), married the Gordon Sisters, first Mary then Margaret. "Ontario, County Marriage Registers, 1858-1869," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:Q2CB-3L4M : 16 March 2018), Hamilton Laury in entry for Hamilton Laury and Margt Gordon, 25 Mar 1861; citing Ottawa, Ontario, Canada, Archives of Ontario, Toronto; FHL microfilm 1,030,062. This record states his mother was Agnes.

UK National Archives under Admiralty
Name: Hamilton Lowry;
Ship's name: HMS Clyde;
Pay book number: SB 77;
Rank: Able Seaman;
Relation: Mother Ann;
When Alloted: 1800;
Remarks: Not stated.
Date: 1798 - 1801
Reference provided by Charles Scott and found here: https://discovery.nationalarchives.gov.uk/details/r/C12196312

Hamilton a former Sea Captain immigrated in 1826, one year after one of his son's. His wife passed away in Ireland or on the ship, not sure which, but she is not with the family in Canada.

The family settled in Fitzroy which bordered Huntley, Carleton area in Ontario, Canada. Hamilton ran a Hotel near Marathon, Ontario and he farmed. It seems hat Hamilton and his brother Michael immigrated to Canada together or within a short time of one another.

The following history is part of an article written for the book "Beyond our Memory ... a history of Fitzroy Township". http://contentdm.ucalgary.ca/digital/collection/p22007coll8/id/196590
Beyond Our Memory Edited by Karen Lewis Runtz. Published by Fitzroy Township Historical; Society, Kinburn, Ontario. 1989.

In 1826, Hamilton along with several of his family came to Canada. Included in the group were his eldest son Savage and Savage's wife Jane. and their 7 month old son Hamilton. Another son had immigrated the year before. Osey, Hamilton's 17 {sic] year old daughter stayed in Ireland one year longer to study with a Doctor because she knew Doctors were scarce. When coming over to join her family the 17 year old was shipwrecked in the Gulf of St. Lawrence and landed on Anticosti Island. All her linens and possessions were lost. (Due to this girls age perhaps this Was Ann? the sister mentioned in Hamilton's sonJames Lowry's Will?)

They settled on Lot 1, Con. 8 in Fitzroy Township, near Marathon. After a career as a Sea Captain, Hamilton at age 60 some, took up farming and running a Hotel which was describe like "a Village". Across from the Hotel, was a building with sleeping quarters and no one was turned away due to being unable to pay.

The Lowry's are purported to be descendants of French Huguenots who fled from France to Great Britain in 1572 during the St. Batholomews Massacres. They then migrated to Scotland and Ireland and finally Canada. Their Surname name was derived from the place they had settled in France (Loir Valley). Years of usage change De Loire to Lowry. The movement to Ireland was preceded by family movement to England then to Scotland. There is another book named "The French Huguenot's in Ireland" by Rev. JWS Lowry which gives more information. This book is still to be located.

Lowry Presbyterian Church, Fitzroy-Huntley Township Line.
A Presbyterian clergyman in Perth, Ontario, Rev. Wm. Bell, heard that the people of this faith in Fitzroy needed a clergy to serve their needs. In 1837, after reaching Fitzroy Harbor, he made his way for 10 miles over a difficult trail to the home of Mr. Hamilton Lowry in a small settlement called Marathon on the Fitzroy-Huntley boundary. Here, Rev. Bell preached and baptized four children. The house was "crowded in all its rooms." Next morning, Rev. Bell preached again to a full house since there were many Presbyterian families who had settled in the two townships. One year later, his successor, Rev. Thomas Wilson, made the journey to the Lowry community where he christened three children. In 1841, Rev. Alexander Mann was inducted into this charge where he served for several years until he was assigned to the Pakenham charge.

Hamilton Lowry donated a small acreage facing the boundary line between Huntley and Fitzroy between 8th and 9th concessions to build a Centre of worship for neighboring families of the Presbyterian faith. By 1845, supported by donations of money and free labor from the parishioners, Lowry church was ready for use. In due time a shelter for horses and rigs was erected on the western corner of the church. Land was marked out between the church and the nearby creek for a cemetery, known to future generations as Lowry Cemetery.

Following a church union in 1925, Lowry Church closed its doors. Mr. Wm. Lytle dismantled the structure in 1935 and used the material to build his home near Carp. The cemetery was subsequently extended across the area where the church and sheds had stood. A black steel fence and gateway was erected around the cemetery in 1976, a bequest of the late Abbie Hanna and a contribution from Mr. Irwin Haskett, a former MLA for Ottawa South.

Hamilton was on land and found in the 1842 Canada Census in Bathhurst Huntley which can be found at the following link. As the story states, his land was on the border of Huntley and Fitzroy.
http://data2.collectionscanada.gc.ca/1842/uc/jpg/004569584_00122.jpg Canada Collections for Huntley and Fitzroy, Upper Canada 1842

Hamilton was found in the 1851 Census. His age was on record as 80. This would put his year of birth as 1771, He was living with a woman named Jane Lowry (his daughter in law who was his deceased son Savage's wife) aged 46 and Robert Lowry (one of Jane and Savage's children) aged 28 and a Servant named Sarah F????? aged 25.http://data2.collectionscanada.gc.ca/e/e094/e002344703.jpg 1851 Canada Collections Fitzroy, Carleton, Ontario.

Hamilton was found in the 1861 Census in the same area. His age is still 80. This would put his year of birth as 1781. His is living with a woman named Sibby or Libby Lowry age 31 and John Lowry aged 1.http: //data2.collectionscanada.gc.ca/1861/jpg/4107388_00061.jpg 1861 Canada Collections Fitzroy, Carleton, Ontario

Hamilton died in 1864 at the age of 101 and was interred in the Lowry Cemetery, Carp, Ottawa Municipality, Ontario, Canada. His stone states he was born in the year 1763

Find book:
"The Gordon's of Goulborn, The Lowry's of Huntley and Fitzroy" by Eliz. M. Gordon.

and the book,

The French Huguenots in Ireland by Rev. J.W.S Lowry.

According to a letter from Uncle Clint Lowry, a "Bruce Lowry" (son Dale) share that this woman Liz. M. Gordon, got a grant to travel and write this 100+ page book. It is about the 6 Gordon Family members who intermarried with 6 Lowry Family members. This Lowry family is about this Hamilton Sr. and his family.

Bruce Lowry says that the family name Lowry may have originally been De Lorrie...and they may have come from the Lorrie River Valley in France. They were part of the Huguenot movement and expelled from France as well and many ended up in England, Scotland and then Ireland. This is common family lore.