Short answers, pulled from the story.
Pope Adrian IV issued the bull in 1155. This document became the legal foundation for English rule, though modern scholars now recognize it as part of the Donation of Constantine forgery.
Henry granted John Lackland his Irish lands at an Oxford parliament in May 1177. Ten-year-old John became Lord of Ireland, establishing the title that would last until 1542.
By 1450, the area under English control had shrunk to a small region around Dublin known as the Pale. The rest of the island remained under various Gaelic kingdoms who frequently fought against Anglo-Norman forces.
Henry VIII changed his title in 1542 when the Crown of Ireland Act passed by the Irish Parliament granted him the new title King of Ireland. He had been excommunicated by the Catholic Church and worried that his Lordship title could be withdrawn by the Holy See.
The transformation from Lordship to Kingdom marked the end of over three centuries of Anglo-Norman rule beginning in 1177. This period concluded with the passing of the Crown of Ireland Act in 1542.