I searched the subscription site Roots Ireland for the surname McLuen in Co. Roscommon and the six records I reviewed were all Church of Ireland and the parish was Bumlin which covers Strokestown. Were the ancestors for the Iowa family Church of Ireland?
I searched on two sites for a baptismal record for Elizabeth McGlenn in Co. Cork and the records that came up were either Glynn/McGlynn in Cork city. I did not find a record for Elizabeth.
I don't believe that McGlynn and McLuen are the same surname.
Civil registration of births started in 1864. I searched on the free site www.irishgenealogy.ie and there were 45 Elizabeth Carney birth records across Ireland from 1864-1870. Only three were in Co. Cork and none of the mothers were Elizabeth.
Sorry, I could not be more helpful. Let me know what questions you might have.