Question: What island is part of the Islands of Furness and has a castle that was used as a base by the Yorkist pretender Lambert Simnel in 1487?

Context paragraphs:
John Estrete: John Estrete, or Strete (died c.1491) was an Irish judge and statesman of the late fifteenth century.  He held the offices of King's Serjeant, Deputy Chief Baron of the Irish Exchequer, and Master of the Coinage of Ireland.  He was a member of the Privy Council of Ireland.  He was a supporter of Gerald FitzGerald, 8th Earl of Kildare, who was almost all-powerful in Ireland for many years, and was prepared to defy the English Crown on occasion.  Despite his close FitzGerald connection Estrete in time gained the confidence of the English Crown, and acted as an intermediary between the Crown and Kildare, notably during the rebellion of Lambert Simnel.

Baron Trimlestown: Baron Trimlestown, of Trimlestown in the County of Meath, is a title in the Peerage of Ireland.  It was created in 1461 for Sir Robert Barnewall, who was the younger brother of Nicholas Barnewall, Chief Justice of the Irish Common Pleas, and younger son of Sir Christopher Bernevall, Lord Chief Justice of the King's Bench in Ireland.  He was succeeded by his son Christopher, the second Baron.  Christopher was implicated in the Lambert Simnel conspiracy, but received a royal pardon in 1488.  His son John, the third Baron, served as Lord Chancellor of Ireland from 1534 until his death in 1538.

Piel Castle: Piel Castle, also known as Fouldry Castle or the Pile of Fouldray, is a castle situated on the south-eastern point of Piel Island, off the coast of the Furness Peninsula in north-west England.  Built in the early-14th century by John Cockerham, the Abbot of neighbouring Furness Abbey, it was intended to oversea the trade through the local harbour and to protect against Scottish raids.  The castle was built using stones from the local beach, and featured a large keep with surrounding inner and outer baileys.  It was used as a base by the Yorkist pretender Lambert Simnel in 1487, but by 1534 it had fallen into ruin and passed into the hands of the Crown.  Sea erosion began to cause significant damage to the castle in the early 19th century.  In the 1870s the castle's owner, the Duke of Buccleuch, carried out extensive restoration work and erected outworks to protect it against further damage from the sea.  In 1920 the castle was given to the town of Barrow-in-Furness and is now in the care of English Heritage.

Martin Schwartz (mercenary): Martin Schwartz (died 16 June 1487) was a German mercenary who died at the Battle of Stoke Field while fighting for Lambert Simnel, a Yorkist pretender to the English throne.

James Keating: Sir James Keating (died after 1491) was an Irish cleric and statesman of the fifteenth century.  He was Prior of the Irish house of the Knights Hospitallers and a member of the Privy Council of Ireland.  Despite his political eminence he was a man of ruthless character and violent temper who once tried to murder a senior judge, and was generally believed to be directly responsible for the death of his designated successor as Prior.  After a long and turbulent career he was removed from office for his treason in supporting the Lambert Simnel Rebellion of 1487, and died in poverty.

John Payne (bishop of Meath): John Payne, Bishop of Meath held that office from 1483 until his death in 1507; he was also Master of the Rolls in Ireland.  He is best remembered for his part in the coronation of Lambert Simnel, pretender to the Crown of England, in 1487.

Piel Island: Piel Island lies half a mile (1 km) off the southern tip of the Furness Peninsula in the administrative county of Cumbria, though historically within Lancashire north of the sands.  It is located at (OS grid ref.  SD233637).  It is one of the Islands of Furness.  It is the location of the English Heritage-owned Piel Castle.

Battle of Stoke Field: The Battle of Stoke Field on 16 June 1487 may be considered the last battle of the Wars of the Roses, since it was the last major engagement between contenders for the throne whose claims derived from descent from the houses of Lancaster and York respectively.  The Battle of Bosworth Field, two years previously, had established King Henry VII on the throne, ending the last period of Yorkist rule and initiating that of the Tudors.  The Battle of Stoke Field was the decisive engagement in an attempt by leading Yorkists to unseat him in favour of the pretender Lambert Simnel.

Lambert Simnel: Lambert Simnel (c. 1477 – c. 1525) was an imposter to the throne of England.  His claim to be the Earl of Warwick in 1487 threatened the newly established reign of King Henry VII (reigned 1485–1509).  Simnel became the figurehead of a Yorkist rebellion organised by John de la Pole, Earl of Lincoln.  The rebellion was crushed in 1487.  Simnel was pardoned and was thereafter employed by the Royal household as a scullion, and, later, as a falconer.

Lambert Simnel (horse): Lambert Simnel (1938–1952) was a British Thoroughbred racehorse and sire, who raced during World War II and was best known for winning the classic 2000 Guineas in 1941.  As a two-year-old he won once and finished second in the Dewhurst Stakes In the following spring he won the 2000 Guineas, beating a field which included the subsequent classic winners Owen Tudor and Sun Castle.  He was beaten when favourite for the Derby and finished unplaced in the St Leger.  He won once as a four-year-old in 1942 before being retired to stud.  He stood as a breeding stallion in England and Argentina with limited success before his death in 1952.

Supporting paragraphs: Piel Castle Piel Island
Answer: Piel Island