The 1865 marriage should give you Clements’ father’s name and occupation. The tithe applotment records for 1832 list 3 Reid farms in Letmacollum. One held by Thomas senior, one by Thomas junior and one by William. One of those is likely Clements’ father and the other 2 could well be related, being in the same small townland. (There were only about 14 farms in the townland in 1864).
http://www.irishgenealogyhub.com/armagh/tithe-applotments/lisnadill-parish.php#.WtrV-hR9eg1
Clements’ birth is before the start of statutory registration in Ireland (1864) so you won’t get a birth certificate for him. You might find his baptism. You haven’t said what denomination he was. But copies of the surviving church records for Lisnadill are in PRONI in Belfast.
PRONI has a conveyance relating to James Reid dated 28.10.1788 ref D285/5
Conveyance. Consideration: £9. 2s. Ruddy and Mary Wright, Monige, Co. Monaghan 1st part, John and Margaret Robinson, Ardmore, Co. Armagh 2nd part, James Reed, Letvicollum, Co. Armagh. Relating to land at Letvicollum (Latmacollum), Co. Armagh.
D285/8 3rd April 1790
Offer to renew lease of land. Thomas Read to James Read. Relating to land at Letmacollum, Co. Armagh
There may be a branch of the Read family in Co. Monaghan judging by this:
D285/9 20th July 1790
Renewal of lease of 25 acres for three lives renewable for ever. Rent: £1.18s. 5d. p.a. Thomas Read, Monage, Co. Monaghan to James Read, Letmacollum, Co. Armagh
D285/11 April 1791
Assignment of Mortgage. Consideration: £200. James Reed, Letmacollum, Co. Armagh 1st part, Thomas Simpson, Ballyards 2nd part, Samuel Carson, Armagh, 3rd part. Relating to land at Letmacollum, Co. Armagh
D285/12 & D285/13 14th March 1792
Lease of 8 acres, 3 perches for 18 years from 1 Nov. 1791 or three lives. Rent: £4. 1s. 10d. plus fees p.a. Clement Read to James Read both of Letmacollum, Co. Armagh. Relating to land at Letmacollum, Co. Armagh
D285/14 & 15 are more leases involving the family, as is T514/15.
T514/16 is another lease and mentions that Thomas Reed of Monage, Co. Monaghan was a linen dealer.
A search of the Registry of Deeds records in PRONI or Dublin may throw up some more deeds relating to Reid and Latmacollum.
You can see that the family were farming in Latmacollum in the 1700s and in all probability they settled there in the 1600s as part of the plantation.
I note from the tithe applotment records that there were 3 or 4 farms in Monage, Monaghan in 1830: Clements (2), James, & Ralph.
http://titheapplotmentbooks.nationalarchives.ie/search/tab/home.jsp
Griffiths Valuation lists a Clement Reed farming in Monage, Co Monaghan in 1858.
I see a few Clement Reed/Read deaths there. One 1865, aged 75, another 16.3.1888, aged 96. The informant was his son another Clement. That Clement died 13.5.1891 at Drumgole. Bachelor aged 40. His probate abstract mentions that he was “late of Monage”, and that his executor was his brother Turner Oliver Read of Roscrea, Co. Tipperary. This looks to be him in the 1901 census:
http://www.census.nationalarchives.ie/pages/1901/King_s_Co_/Gorteen/Dungar/1467229/
The above family was Church of Ireland.