EI-
The Irish authorities do require some connection to Ireland to permit registration athough it is less stringent than most other countries. It is common for special purpose companies to be set up and registered in Ireland to own aircraft. The fact that many lessors locate in Ireland is because of the tax advantages of the ISFC in Dublin and the Shannon trade area. These advantages are I understand coming to an end. In addition Ireland benefits from very favourable double taxation treaties with many countries.
Certainly EUJet and Ryanair would pass all the required connectivity tests for registration. The lessor community is very large in Ireland and includes GECAS,Orix, RBS. Some airlines have set up Irish subsidiaries for specific aircraft financings including Iberia.
Although initially subsidised by the Irish tax payer, their policy has attracted jobs and investment.