The drawing - a rare work from Lawrence's early career - has recently been identified as depicting Mary Hamilton, the wife of one of his best friends, William Hamilton, a fellow Royal Academician. It is on display at the British Museum in London in the Masterpieces of Portrait Drawing, 1450-1800 show, but, thanks to a successful fund-raising drive to stop it going overseas, will join the museum's collection permanently.
The drawing is significant because it highlights a little-known part of the history of the Royal Academy in London, which exhibited such drawings alongside its members' paintings in the 18th and 19th centuries to popular acclaim. They were highly favoured and widely discussed, with reviews in all of the newspapers, according to Kim Sloan, a British Museum curator.
But, because such drawings are less highly valued today, relatively few of those originally exhibited at the Royal Academy have been identified. This is a rare example.
The Government issued a temporary export ban to give the British Museum time to raise £165,000 to buy it. The National Heritage Memorial Fund, a fund of last resort for national treasures, and the National Art Collections Fund charity, both gave grants to help.
Ms Sloan said they were particularly keen to have the work as it was arguably the most beautiful female portrait of its type remaining in the UK.
It was certainly the most important British drawing to be added to the British Museum collection for years. A large number of Lawrence's works are in private hands or have been sold abroad, particularly to America during a vogue for his art at the beginning of the 20th century. British museums and galleries were "notoriously lacking in fine examples of Lawrence's works," Ms Sloan added.
Stephen Johnson, director of the National Heritage Memorial Fund, said: "It would have been a huge loss if it had left these shores for good."
Thomas Lawrence was born in Bristol in 1769, the son of an innkeeper. He developed a reputation for painting and had his own studio by the age of 12. In 1787, he became a student of the Royal Academy and two years later, aged 20, he painted Queen Charlotte, the wife of George III.
This drawing of Hamilton, who used to read to him and her husband as they drew alongside each other, was made at around the same time. It stayed in her family's possession until it was sold at auction three years ago.
The 19th-century master Delacroix described Lawrence's portraiture as "incomparable" and only Ingres was regarded as his rival in the genre. He was knighted in 1815 and became president of the Royal Academy five years later. Hugely popular in his lifetime, he commanded high fees. He died in 1830.