Fitton was the eldest son of William Fitton of Awrice, County Limerick and his wife Eva Trevor, daughter of Sir Edward Trevor of Denbighshire. He was the great-grandson of Sir Edward Fitton, Vice-Treasurer of Ireland. The Irish Fittons were a junior branch of the Fittons of Gawsworth Old Hall, Cheshire; the dispute over the ownership of Gawsworth was to pre-occupy Alexander for most of his life. He married Anne Joliffe, daughter of Thomas Joliffe of Worcestershire and they had one surviving daughter; Anne died in 1687.
He entered Gray's Inn in 1654 and the Inner Temple in 1655; he was called to the Bar in 1662. Since he quickly became embroiled in the Gawsworth inheritance claim, it is unclear if he ever practised as a barrister, which later led to questions about his suitability for judicial office, quite apart from the obvious objection of his criminal conviction.
Sir Edward Fitton, 2nd Baronet, of Gawsworth, died in 1643 without issue; he had seven sisters, but the nearest male Fitton heir was Alexander's father William. In 1641 Edward made a settlement creating an entail in favour of William and his male heirs. This was done against the violent protests of Charles Gerard, son of Edward's sister Penelope, who was the nearest heir by blood. After Edward's death the Gerards tried to hold Gawsworth by force; but the progress of the English Civil War turned in the Fitton family's favour: as a staunch Royalist Gerard's own estates were forfeited and he left England about 1645, leaving the Fittons in possession until the Restoration.
By 1662 Gerard, now Baron Gerard of Brandon, had recovered his own estates and was in high favour at Court; inevitably he laid claim to Gawsworth, bringing a lawsuit in the Court of Chancery in which he exhibited a will supposedly made by Edward Fitton just before his death. Alexander Fitton, rather than simply relying on the entail by which he succeeded as his father's heir, produced a deed which on the face of it made the settlement on his father irrevocable. Gerard then dramatically produced a notorious forger, Abraham Granger, who testified that he had forged the deed on Fitton's behalf. The Court ordered a jury to find the facts: they found that the deed was indeed a forgery, and while Fitton managed to get a second hearing before a Cheshire jury, the result was the same. Lord Gerard duly took possession of Gawsworth.
Which party (if either) was legally or morally in the right it is now difficult to say: it is suspicious that both parties were relying on documents whose very existence had been previously unknown, and it is quite possible that both the will and the deed were forged. Fitton proceeded to make a serious mistake in publishing a pamphlet directly accusing Gerard of winning the case by bribing and threatening witnesses, and including what purported to be Granger's confession that he had committed perjury.Fitton was perhaps unaware that to libel a peer was scandalum magnatum, a criminal offence. The House of Lords took a serious view of the matter and Fitton was committed to the King's Bench Prison until if ever he produced Granger to confirm his story. Given Granger's character, it is hardly surprising that Fittton never did produce him, and he might well have remained in prison for life. As it was (though accounts differ) he may still have been in prison in 1687. The petition to the House of Commons of England in 1668 mentioned in Pepys' Diary cane to nothing as did an attempt to prosecute Gerard's witnesses for perjury. The disgrace of Gerard, now Earl of Macclesfield, who supported the Exclusion Bill and was later suspected of complicity in the Monmouth Rebellion, encouraged Fitton to make one last effort to recover Gawsworth; somewhat surprisingly his case was dismissed for undue delay. The affair however caused the new King James II to look favourably on Fitton.
In 1687 the Irish Lord Chancellor Sir Charles Porter expressed reservations about the King's policy of toleration of Catholics and was dismissed; while Richard Nagle, the Attorney General for Ireland, a Roman Catholic, put forward his own claim to the office, James was persuaded that Fitton, a Protestant, would be a better choice. Fitton thought it advisable to convert to Catholicism. As Lord Chancellor he was accused of ignorance, prejudice and bias against Protestants, although some historians have questioned the accuracy of these charges. When James II arrived in Ireland Fitton presided over the Patriot Parliament of 1689; he was given a barony and inevitably chose the title Baron Fitton of Gawsworth. When James fled Ireland after the Battle of the Boyne Fitton was appointed Lord Justice of Ireland and acted on behalf of the King in his absence; the following year he joined James in France, although it is unclear if any proceedings were pending against him. He died at St. Germain in 1698.
Fitton has been treated harshly by historians, especially Thomas Macaulay, who dismissed Fitton as a "pettifogger" without legal ability or commonsense, and unfit by reason of his imprisonment for libel, and the charge of forgery to hold any office. O'Flanagan writing in 1870 took a more charitable view, stating that he had examined Fitton's decrees and found in them no evidence of ignorance or incapacity; on the contrary, they appeared to be the work of an experienced equity judge. On the accusation of forgery, the safest view is that Gerard and Fitton were both guilty of it; Elrington Ball remarks that "bad as Fitton's character may have been, it can scarcely have been worse than that of Lord Gerard".