Of course it's public domain, regardless of who may claim otherwise.

The version that Lighter mentioned above is here:- Lord Franklin performed by Micheál Ó'Domhnaill and Kevin Burke with vocals from sister Triona, and bouzouki from Donal Lunny.

Sir John Franklin's wife Lady Jane was entitled to be called "Lady Franklin" because her husband was a baronet. Somewhere along the line somebody mistakenly assumed that Sir John was a peer.

The tune is variously used for "McCaffery", the "Croppy Boy" and an Irish song "Cailín Óg a Stór".

http://en.wikipedia.org/wiki/Lady_Franklin%27s_Lament has much detail, including a multitude of artists who have recorded the song.

Ross