The issue of Lyme disease is not confined to the National Parks. Ticks are widespread in the country and areas of rough vegetation and forestry and are not at all confined to National Parks, Nature Reserves or state lands. Ticks can be found on a variety of domesticated and wild animals including sheep, goats, horses, cattle, dogs, deer, rodents and various wild mammal species.
With regard to signage and notices, information on ticks for members of the public intending to visit the Park is contained in the health and safety section of the dedicated website http://www.killarneynationalpark.ie/visit/health-safety and is available in the visitor centre at Killarney House.
Information on Lyme Disease is available from the HSE and, their booklet:
http://www.hpsc.ie/a-/vectorborne/lymedisease/informationforthepublic/Lyme%20DL%20April2017%20-%20D2.pdf contains useful information in this regard.
The National Parks & Wildlife Service of my Department would be willing to engage with the Local Authority on any county-wide initiatives they (or the HSE) wish to propose.