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.
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.
For members of the public who intend on visiting National Parks, information on ticks is contained in the health and safety section of the park website. For example, with regard to Killarney National Park, information is available on the dedicated Park website at
http://www.killarneynationalpark.ie/visit/health-safety and is also available in the visitor centre at Killarney House.
The issue of warning notices is a matter for the HSE/Local authorities to consider. Any such signs would need to be countywide as opposed to specifically located in particular National Parks or Nature Reserves. This is not an issue which is localised to National Parks or state lands. It is an issue throughout the countryside.
The National Parks & Wildlife Service of my Department is willing to engage with the Local Authorities on any county-wide initiatives they (or the HSE) wish to propose.