Ireland in the century prior to the Anglo-Norman invasion of 1169 is probably best described as a national kingdom lacking a settled monarchy, the kingship being disputed by three regional dynasties.
The Lordship of Ireland (1171-1541) was a nominally all-island Irish state created in the wake of the Norman invasion of the east coast of Ireland in 1169, an area that became known in the later middle ages as the 'pale' or 'Pale of Dublin' from its defences in imitation of the earlier-named 'Pale of Calais'. Its authority was never extended throughout the island of Ireland at any time during its existence but was restricted to the Pale. It owed its origins to the decision of a Leinster dynast, Diarmuid MacMorrough, to bring in a Norman knight based in Wales, Richard de Clare (alias 'Strongbow'), to aid him in his battle to regain his throne, after being overthrown by a confederation led by the new Irish High King (the previous incumbunt had protected MacMurrough). Henry II of England, who reigned over England and ruled over parts of France, invaded Ireland to control de Clare, whom he feared was becoming a threat to the stability of his own kingdom on its western fringes (there had been earlier fears that Saxon refugees might use either Ireland or Flanders as a base for a counter-offensive after 1066); ironically, much of the later Plantagenet consolidation of South Wales was in furtherance of holding open routes to Ireland. Having captured a small part of Ireland on the east coast, Henry used the land to solve a dispute dividing his family. For while he had divided his territories between his sons, one son, nicknamed 'John Lackland' (or 'Jean Sans-terre' as Henry and his family regarded themselves as French and spoke the language), was left without territory, hence the nickname. Henry granted John/Jean his captured Irish lands, becoming Lord of Ireland (Dominus Hiberniae) in 1185, with the territory becoming the Lordship of Ireland.
Fate however intervened in the form of the deaths of John/Jean's older brothers. As a result, he became King John of England, and the Lordship of Ireland, instead of being a separate area governed by a minor English prince, became a territorial possession of the English Crown.
English monarchs continued to use the title 'Lord of Ireland' to refer to their conquered lands on the island of Ireland. The title was changed by an Act of the Irish Parliament governing these lands in 1541, when on Henry VIII's demand, he was granted a new title, King of Ireland, with the state renamed the Kingdom of Ireland.
Norman Davies, The Isles: A History (Palgrave-Macmillan, 1999) (ISBN 033376370X)