Loads of Irish people buy abroad!
ou may want to contact this company "Your Property Abroad", as they are an Irish company who specialise in finding Lanzarote properties for sale based on what you want. They don't own any properties and have a big network of Lanzarote agents with whom they've worked for years. They'll sort you out and can answer all your questions. They also arrange for you to meet with an agent when you're over etc.
The owner's name is Gary and if you enquire online through the contact form he'll contact you: yourpropertyabroad . com
Hope this helps! Good luck with your property search