Margaret Clark’s chapter in UCLan’s Harris Papers volume on Joseph Livesey contains a tantalising reference to one of his sons: ‘Alfred … remains an obscure figure, with a question unanswered as to why he, of all the brothers, left virtually no estate in his will’.  Dr Clark did not have access to the riches that the internet is now serving up; if she had she would have discovered that Alfred committed suicide, depressed and facing financial ruin.
His death was reported in a number of newspapers that can now be accessed on line (Lancashire Library membership gives free access). It was, of course, reported in the Preston Guardian, which is not available on line; I will transcribe the Guardian report when I visit Lancashire Archives.
The Lancaster Gazetter published on 18 April, 1888, carried the following report (wrongly identifying Alfred as Joseph’s youngest son) :
Suicide of a Liverpool Merchant. — Mr Alfred Livesey, a member of the firm of Messrs. Alfred Livesey and Co., provision merchants, Mathew-street, Liverpool, committed suicide on Saturday by cutting his throat. Deceased lived at 4. Regent-road, Great Crosby. About two o’clock on Saturday he escorted his wife to the house of a friend, and, leaving her there, promised to return for her at five o’clock. He did not, however, at the appointed time make his appearance. Mrs Livesey returned home alone. A servant subsequently found Mr Livesey lying on the floor of the hencote, bleeding from a wound in the throat. Dr. Paget pronounced him dead. The wound had evidently been inflicted with a razor, which was found by the side of deceased. Mr Alfred Livesey was the youngest son of the late Joseph Livesey, of Preston. He was in business with his father and brother for many years, as cheese merchants, and a few years ago on giving up business in Preston, Mr Livesey commenced the American trade at Liverpool. It is reported that he has sustained heavy losses, and that he has for some time back been greatly depressed.
Alfred was born in 1833, Joseph Livesey’s eighth son to survive infancy. Little can be gleaned about Alfred from Joseph’s autobiography, nor about any of his other children. Alfred and his brother Newton joined the family cheese business as partners with their father, and the two brothers continued in business together after their father withdrew from the partnership in 1874. 
Dr Clark writes that another brother, Howard, ‘took over the business interests of his brothers Newton and Alfred in their retirement’. But clearly Alfred had not retired, even if he had withdrawn from the family partnership, since he was still in business in Liverpool at the time of his death.
In 1871 Alfred, then aged 37, and his wife, Hannah, were living at 9 Bushell Place, Preston, with their two young sons and two servants (Ancestry website). In 1881 Alfred and Hannah were living in Great Crosby with their two sons and a servant (Ancestry website). Earlier in life he had kept pedigree dogs, winning prizes at local agricultural shows: ‘The bull terriers were good, but none could compare with the dog shown by Mr. Alfred Livesey, of Preston, and which dog took the first prize of its class at the Preston Guild.’  At other events he was called on to judge the dogs on show.  At the mayoral ball held at the Corn Exchange in 1877 Alfred and his wife were among the guests along with other members of the Livesey family. 
His father would not be in attendance, since he resolutely refused to attend any occasion at which alcohol might be served, as he explained in his autobiography (Chapter Eleven):
For years together I have never attended a “party,” though often invited, and when the mayors of the borough have sent me invitations to their “dinners” or festive gatherings, I have always declined going. I had a strong objection to be found at any gathering where wine drinking was sure to be prominent, and where I could not with propriety protest against it.
 Ian Levitt, ed., Joseph Livesey of Preston: Business, Temperance and Moral Reform (University of Central Lancashire, 1996), 24.
 ‘LOCAL INTELLIGENCE’, Lancaster Gazetter P2, 18 April 1888, British Library Newspapers, https://link.gale.com/apps/doc/R3210357702/BNCN?sid=bookmark-BNCN&xid=475cbc5f.
 ‘Page 782 | Issue 24067, 20 February 1874 | London Gazette | The Gazette’, https://www.thegazette.co.uk/London/issue/24067/page/782.
 ‘BROUGHTON AND GOOSNARGH AGRICULTURAL SOCIETY’, Preston Chronicle P4, 26 September 1863, British Library Newspapers, https://link.gale.com/apps/doc/Y3207462410/BNCN?sid=bookmark-BNCN&xid=673f3790.
 ‘ANNUAL MEETING OF THE BROUGHTON, &c., AGRICULTURAL SOCIETY’, Preston Chronicle P7, 15 September 1866, British Library Newspapers, https://link.gale.com/apps/doc/Y3207468580/BNCN?sid=bookmark-BNCN&xid=309610df.
 ‘THE MAYOR’S BALL’, Preston Chronicle P4, 10 February 1877, British Library Newspapers, https://link.gale.com/apps/doc/Y3207486359/BNCN?sid=bookmark-BNCN&xid=19ee2631.