Caroline:
Welcome to Ireland Reaching Out!
I searched the subscription site Roots Ireland and was not able to find a Lawrence McGann baptismal record around 1835 in Co. Galway. Also, did not find a Margaret McGann baptismal record with father Lawrence. I assume she was born 1855-1860? Likely their parish does not have records back to that time period. From the 1855 Griffiths Valuation head of household listings, it appears that most of the McGanns were from the southeast part of Co. Galway. There were no Lawrences listed.
Do you have any other family information? Did Lawrence remain in Ireland?
You may want to add Margaret's story to our XO Chronicles site and possibly someone will see a connection.
https://www.irelandxo.com/ireland-xo/history-and-genealogy/ancestor-dat…
Have you considered DNA testing?
Roger McDonnell