Question: William Stanley, 3rd Baron Monteagle resided in a castle located in what valley?

Context paragraphs:
Hugh Wedgwood, 3rd Baron Wedgwood: Hugh Everard Wedgwood, 3rd Baron Wedgwood (20 April 1921 - 25 April 1970) was the third Baron Wedgwood of the pottery dynasty.  He was the son and only child of The Hon. Francis Wedgwood (later 2nd Baron) and his wife Edith May Telfer, daughter of William Telfer of Glasgow.  He was the great-great-great-great-grandson of the potter Josiah Wedgwood.  Like his father, he was educated at Bedales School.  During the Second World War he served as an officer in the Kenya Regiment.  In 1949 he married Jane Weymouth Poulton, daughter of W.J. Poulton of Kenjockety, Molo, Kenya; they had one son, Piers and two daughters.  He was a farmer in Hillwood, Molo, Kenya, 1941–1964.  Upon his father's death in 1959 he succeeded his father as the 3rd Baron Wedgwood.  Upon his own death in 1970, the Barony passed to his son Piers.

Ralph Mansfield, 4th Baron Sandhurst: Ralph Sheldon Mansfield, 4th Baron Sandhurst, OBE (19 July 1892 – 1964) was the son of John William Mansfield, 3rd Baron Sandhurst.  Mansfield became 4th Baron Sandhurst upon the death of his father, John William Mansfield, the 3rd Baron Sandhurst, in 1933.

William Parker, 4th Baron Monteagle: William Parker, 13th Baron Morley, 4th Baron Monteagle (15751 July 1622) was an English peer, best known for his role in the discovery of the Gunpowder Plot.  In 1605 Parker was due to attend the opening of Parliament.  He was a member of the House of Lords as Lord Monteagle, the title on his mother's side.  He received a letter: it appears that someone, presumably a fellow Catholic, was afraid he would be blown up.  The so-called Monteagle letter survives in the National Archives (SP 14/216/2), but its origin remains mysterious.

William Stanley, 3rd Baron Monteagle: William Stanley, 3rd Baron Monteagle (1528–1581), of Hornby Castle, Lancashire, was an English politician.

Marquess of Sligo: Marquess of Sligo is a title in the Peerage of Ireland.  It was created in 1800 for John Browne, 3rd Earl of Altamont.  The Marquess holds the subsidiary titles of Baron Mount Eagle, of Westport in the County of Mayo (created 10 September 1760), Viscount Westport, of Westport in the County of Mayo (created 24 August 1768), Earl of Altamont, in the County of Mayo (created 4 December 1771), Earl of Clanricarde (created 1800) and Baron Monteagle, of Westport in the County of Mayo (created 20 February 1806).  All these titles are in the Peerage of Ireland, except the Barony of Monteagle, which is in the Peerage of the United Kingdom.  The latter peerage entitled the Marquesses to a seat in the House of Lords prior to the House of Lords Act 1999.  The Earldom of Clanricarde was inherited by the sixth Marquess in 1916 according to a special remainder in the letters patent.

Mary Brandon, Baroness Monteagle: Lady Mary Brandon, Baroness Monteagle (2 June 1510 – between 1540/1544), was an English noblewoman, and the daughter of Charles Brandon, 1st Duke of Suffolk, by his second wife, Anne Browne.  Mary was the wife of Thomas Stanley, 2nd Baron Monteagle, by whom she had six children.

Baron Stanley of Alderley: Baron Stanley of Alderley, in the County of Chester, is a title in the Peerage of the United Kingdom.  It was created in 1839 for the politician and landowner Sir John Stanley, 7th Baronet.  Upon his death in 1850, he was succeeded as 2nd Baron Stanley of Alderley and 8th Baronet of Alderley Hall by his son Edward, who was a prominent Liberal politician and notably served as President of the Board of Trade, Postmaster General and had in 1848 been created Baron Eddisbury, of Winnington in the County Palatine of Chester, in his own right.  His wife Henrietta was a prominent campaigner for women's education.  After his death, the Stanley of Alderley and Eddisbury baronies remained united; most holders have since chosen to be known as "Lord Stanley of Alderley".  The 3rd Baron Stanley of Alderley had a career in the Diplomatic Service; as he was childless he was succeeded by his younger brother, the 4th Baron.  He was Liberal Member of Parliament for Oldham.  In 1909, the 4th Baron Stanley of Alderley acquired a further title when he succeeded his first cousin once removed, the Earl of Sheffield, according to a special remainder and thus inherited the title of 4th Baron Sheffield.  After his death the titles passed to his son, the 5th Baron Stanley of Alderley.  He was Liberal Member of Parliament for Eddisbury and also served as Governor of Victoria.  His eldest son, the 6th Baron Stanley of Alderley, sold the family seat of Alderley Hall in 1938.  He was married four times, the second time to Sylvia Ashley.  On his death the titles passed to his younger brother, who preferred to be known as Lord Sheffield.  He only held the titles for three months.  s of 2013 the titles are held by the latter's cousin, the 9th Baron Stanley of Alderley, who succeeded his father in that year.  He is the grandson of the Hon. Oliver Hugh Stanley, youngest son of the 4th Baron.

Hornby Castle, Lancashire: Hornby Castle is a country house, developed from a medieval castle, standing to the east of the village of Hornby in the Lune Valley, Lancashire, England.  It occupies a position overlooking the village in a curve of the River Wenning.  The house is recorded in the National Heritage List for England as a designated Grade I listed building.

Thomas Burgh, 3rd Baron Burgh: Thomas Burgh, 3rd Baron Burgh KG ("c." 1558–14 October 1597) 3rd Baron Borough of Gainsborough, "de jure" 7th Baron Strabolgi and 9th Baron Cobham of Sterborough was the son of William Burgh, 2nd Baron Burgh and Lady Katherine Clinton, daughter of Edward Clinton, 1st Earl of Lincoln and Elizabeth Blount, former mistress of King Henry VIII.  He was one of the peers who conducted the trial of the Duke of Norfolk in 1572.

Thomas Spring Rice, 3rd Baron Monteagle of Brandon: Thomas Spring Rice, 3rd Baron Monteagle of Brandon

Supporting paragraphs: William Stanley, 3rd Baron Monteagle Hornby Castle, Lancashire
Answer: the Lune Valley