Hi T M Healy,
I found a few more siblings but no record for Michael.
Thomas November 2 1872
Ellen November 3 1874
Catherine July 8 1877.
I checked the Tithe Applotments of 1827 and found the only land owner in the townland of Aghimma was a Thomas Lynch.
http://titheapplotmentbooks.nationalarchives.ie/reels/tab//004625673/00…
I also checked Griffith's Valuation of 1850s and found a Margaret Buckley leasing a house and around an acre of land from Thomas Lynch.
http://www.askaboutireland.ie/griffith-valuation/index.xml?action=doNam…
This is a link to a map of the area around that time.
http://griffiths.askaboutireland.ie/gv4/single_layer/i8.php?lat=&longt=…
In the 1901 Census I found the Dennihan family living in Ahimma. Daniel and Catherine's daughter Margaret married Michael Dennihan.
http://www.census.nationalarchives.ie/reels/nai000877104/
The family were still there by the time of the 1911 census.
http://www.census.nationalarchives.ie/reels/nai002485756/
This family is the only direct link I could find to your ancestors.
Hope this helps.
Regards,
Joan Holland