Many thanks for your post to the IrelandXO message board. There is a very active local historical society in Galway which will be able to assist you with names of Lynch families who resided in the castle. You might also check out the Landed Estates database which also listed information about families and their residences:
http://landedestates.ie/LandedEstates/jsp/property-show.jsp?id=786 This is the link for Lydacan Castle. You will see that it also refers to families who were associated with the property over the years.
If you need any further assistance, please let us know.
All the best,