Hi Cady,
Sorry I am only getting back to you now, I only visit here now and again.
To answer your more general question first, there is no specific CFS/ME specialist in Ireland, and from my own experiences I have not come across any doctor who is successfully treating people, however others on here might different experiences.
What there is however is a number of doctors from varying backgrounds (Infectious disease/ allergies/ endocrine/ gastro) dabbling in the area of CFS, both for their own curiosity and probably more pertinently their bank balance.
Now, not knowing your specific situation and how you were diagnosed with CFS, somebody like John Lambert might indeed be able to treat you if you suspect an infectious disease component.
However, as I have found to my own detriment, many of these doctors, whether acting in good faith or not, are pigeon holed in their specific sub-discipline and often find it hard to look beyond say the symptoms you may have in that particular area.
Looking at John Lambert's website, he seems to be very much focused on infectious disease, with a particular focus on Lyme treatment, however his testing and treatment seems to follow the conventional ELISA/Western Blot protocols, with a standard months dose of relevant antibiotics. However he does seem aware of the testing going on in Germany
http://www.rte.ie/news/2016/1115/831747-lyme-disease/
Lyme testing and treatment in and of itself is a very controversial area, as I am sure you have seen on here so tread carefully, and perhaps start with what tests your GP can run for you first before looking further a field.
If you have any further questions about traveling abroad feel free to ask and check out what specialists in Europe such as KDM are doing.