Hi Sue,
It's a good thing that Archibald Lawless is a very distinctive name. This will really help in your research. It's difficult to start researching your family tree with a more precise place of origin, but a name like that will really help you a lot.
Civil registration records are available from the General Register Office (GRO). These start from 1864. You can access the website here: http://www.groireland.ie/research.htm
Without a more precise location I cannot recommend church records to you as yet. If you knew a date of death, I could suggest you check local newspapers for information about the death of Archibald.
Did you check the Uk National Archives http://www.nationalarchives.gov.uk/ for information from their move to Wales? They may have left more clues.
You could also try checking the land records called the Tithe Applotment Books (1823-38) or the later Griffith's Valuation (1848-64). Griffith's is freely available here: www.askaboutireland.com or here: www.failteromhat.com Failte Romhat has lots of other useful links you could try looking at.Tithe Applotment Books (1823-38). Microfilm copies of the books for all of Ireland are available at the National Archives of Ireland (NAI) http://www.nationalarchives.ie/genealogy1/genealogy-records/tithe-applotment-books-and-the-primary-griffith-valuation/ or the Church of Latter Day Saints (LDS).
I am sure that those names would ring a bell or two in the Offaly area, so hopefully someone there will be able to help you out further.
Please make sure you link anyone else in your family who is interested in their Irish heritage to our site - and indeed anyone else you know of Irish heritage.
Kind regards,
Sinead Cooney
Genealogist (Ireland XO)
