You are entitled to
1. The most appropriate ticket
2. Your entitlement (if such is possible) to a through ticket to avail of the protections and rights of EU rights.
In the case of Dundalk - Kildare a single ticket for the entire journey is the cheapest ticket and includes the Luas
We have had this argument with Irish Rail, on paper you can travel without a ticket, but I would advise you carry a previously used ticket for investigation
We are aware of others who tried to enforce their rights but got fined.