Gallowglass Books here in Duncan, B.C., Canada (http://www.gallowglassbooks.com/) has a vg copy for C$50 of the 1st ed. of Lord Fisher's autobiography, titled "Records" (pub. 1919 by Hodder & Stoughton). I browsed thro' that book today after seeing your posting. Here in essence is what he says about his family background:
John Arbuthnot Fisher, born Jan 25, 1841 at Rambodde, Ceylon. Father William Fisher was a Capt. in 78th Highlanders, serving in Ceylon as ADC to Governor Sir William Horton. Lady Wilmot Horton (of whom Lord Byron wrote his famous lines beginning "She walks in beauty like the night...")was Lord Fisher's godmother, and Sir Robert Arbuthnot, Commander of H.M. troops in Ceylon, was godfather (an editor's note at the end of the book states this; Fisher however mentions his godfather as having been Major Thurlow of the 90th Foot).Lord Fisher's mother was Sophia, daughter of Mr. A. Lambe of New Bond St., London, and a grandaughter of Alderman Boydell, a famous engraver, who became Lord Mayor of London. Another grandfather of Sophia was one of Nelson's Admirals.
The Fisher family has a long-time burial plot at Packington Church, Warwickshire. A Sir Clement Fisher (d. 1683)was married to jane Lambe, who rescued the fleeing King Charles I by disguising him as her groom and riding behind him on a pillion to Bristol. The baronetcy lapsed when his successor could not afford to pay the Pds. 500 fee to take it up. Another Fisher ancestor contributed a wing to Balliol College, Oxford. Four generations of Reverend John Fishers were rectors in Bodmin, Bornwall, beginning with the first John Fisher in this particular line, born 1708. Lord Fisher's own grandfather was Rector of Wavenden, Bucks. where there is a tablet in the Church commemorating his brother who died close to the Duke of Wellington at the Battle of Waterloo (1814); Lord Fisher owned a watch with a dent caused by the fatal bullet, that the Iron Duke had ordered to be returned to the Fisher family after the victory. Lord Fisher's uncle, also John Fisher, was a Fellow of Magdalen College, Cambridge for over 60 years.
In the very first sentence of his autobiography, Lord Fisher goes out of his way to trounce the rumour that he was actually the son of a "Cingalese princess". he states that his parents married for love, rather than money. Indeed, the high-flying Fishers rather looked down on the "mercantile" Lambes.