Great site and great resource. Was just listening to the one labeled Humours of Drinagh/ The castebar jig. I think that first tune is actually Trip to Athlone. You might want to check with session.org, but I think thats right.
First one is definitely The Trip to Athlone aka The Newport Lass. Recorded by Noel Hill and Tony MacMahon on the famous “In Knocknagree” following The Humours of Drinagh.