According to her article in thepeerage, she was born in 1701 and died childless in 1739.Also, according to the peerage, she was the youngest child and daughter. However, Wikipedia's article about Charles, 3rd Earl of Carlisle, she was the eldest surviving daughter who married Nicholas Lechmere, 1st Baron Lechmere, by whom she had no issue.
These are Sotheby's auction notes for this portrait: "The sitter in this beautiful and exotic portrait is Lady Elizabeth Howard (1701-1739), daughter of Charles Howard, 3rdEarl of Carlisle (c.1669-1738), the eldest son of Edward, 2nd Earl of Carlisle (c.1646–1692), and his wife, Elizabeth (1646–1696), the daughter of Sir William Uvedale of Wickham, Hampshire, and the widow of Sir William Berkeley. In 1701 the 3rd Earl commissioned Sir John Vanbrugh (1664-1724) to build Castle Howard, the magnificent baroque mansion in Yorkshire.
Demonstrating a singular and free spirit which would come to characterise her later years, Lady Elizabeth married Nicholas Lechmere, 1st Baron Lechmere (1675-1727), at the age of eighteen against her father's wishes. Lechmere, an eminent lawyer who had been appointed Solicitor General and Chancellor of the Duchy of Lancaster in 1717, was the second son of Edmund Lechmere and his wife Lucy of Hanley Castle. It was during this marriage that Lady Elizabeth established a reputation for herself as a notorious and inveterate gambler running up debts that at one stage were rumoured to be in the region of a staggering £5,000 and £10,000. As her friend and confidante Lady Mary Wortleyy Montagu (1689-1762) remarked in a letter to Lady Mar dated September 1725, '...The discreet and sober Lady Lechmere has lost such Furious sums at the Bath...particularly £700 at one sitting'.
With support waning from her husband and father, her debts mounted and her attempted suicide was the talk of London in February 1726. As Lady Mary continues in a letter, again addressed to Lady Mar, dated to 3 February 1726: 'But the melancholy Catastrophe of poor Lady Lechmere is too extraordinary not [to] attract the attention of ev'ry body. After having play'd away her Reputation and fortune, she has poisoned her selfe-this is the Effect of Prudence!'. Lady Mary Wortley Montagu was a childhood friend and neighbour of the present sitter, affectionately referring to her as Lady Betty Howard in a letter describing a shared visit to York races in 1714. Best remembered for the lively prose of such letters, Lady Mary travelled to Turkey in 1717 accompanying her husband, the newly appointed ambassador. Gaining unprecedented access and insight into the workings of the Ottoman Empire, she played a hugely significant role in recording and shaping European perceptions of the East. Her vivid descriptions of Turkish fashions soon worked their way west and she was responsible for reigniting the vogue for Turquerie across Europe; a vogue which accounts for the oriental masquerade costume seen in this portrait.
Following the death of her first husband in 1727, Lady Elizabeth married Sir Thomas Robinson (1702/3-1777), the eldest son of William and Anne Robinson of Rokeby Hall, Yorkshire. As an amateur architect and advocate of the recent craze for Neo-Palladianism, Robinson redesigned Rokeby in accordance with Palladio's Quattro libri, and worked at Castle Howard proposing designs for a west wing in 1753. Soon after their marriage, Robinson made a tour of the continent with his new wife. Together they travelled via Paris to Italy where they were presented to the King of Sardinia in Turin before being entertained by the British minister Edmund Allen. From Turin they went to Genoa and to Milan before travelling to Rome via Florence. It was presumably in Rome that she sat for her portrait to Knapton who was based in Italy from 1725 to 1732 travelling frequently to Rome. Lady Elizabeth would have been aged twenty nine by the time she reached the city and her appearance in this picture verifies this and supports the theory that this was painted on the continental tour.
Upon his return from Italy Knapton became one of the first fashionable portraitists to use crayon, playing an important role in establishing the medium in England. Nothing is known of his work and little of his activities before 1736 when he became a founder member of the newly formed Society of Dilettanti, with the official title of Painter to the Society. Between 1741 and 1749 he painted a remarkable series of 23 portraits of member of the society in a variety of fancy dress (apart from the Duke of Bedford) for which he is best known. Having given up painting in 1755, he resigned as a Dilletante in 1763 becoming surveyor and keeper of the King's pictures until his death in 1778. His works in oil are rare and mostly date between 1741-51. This picture is an important addition to his oeuvre, and stands testimony to the skill and facility that established a distinguished career in England. Knapton is represented in a number of important National Collections such as Chatsworth, The National Portrait Gallery, London Dulwich Art Gallery, The Metropolitan Museum, New York, the Royal Collection Windsor and Buckingham Palace."