He married Alice Hopkinson (1899–1989), a cousin of a friend who had been killed in the war, in 1921, They had four children, Stephen Lawrence (1923–2014), David william (1926–2005), Margaret Alice, born 1931, (who married Mark Heath) and Patience Mary, born 1935. Alice was on the staff at Withington Girls' School until Bragg was appointed Director of the NPL in 1937. She was active in a number of public bodies and was elected Mayor of Cambridge.
After beginning his studies at St Peter's College, Adelaide in 1905, Bragg went to the University of Adelaide at age 16 to study mathematics, chemistry and physics, graduating in 1908. In the same year his father accepted the Cavendish chair of physics at the University of Leeds, and brought the family to England. Bragg entered Trinity College, Cambridge in the autumn of 1909 and received a major scholarship in mathematics, despite taking the exam while in bed with pneumonia. After initially excelling in mathematics, he transferred to the physics course in the later years of his studies, and graduated with first class honours in 1911. In 1914 Bragg was elected to a Fellowship at Trinity College – a Fellowship at a Cambridge college involves the submission and defence of a thesis.
Bragg was commissioned early in the First World War in the Royal Horse Artillery as a second lieutenant of the Leicestershire battery. In 1915 he was seconded to the Royal Engineers to develop a method to localize enemy artillery from the boom of their firing. On 2 September 1915 his brother was killed during the Gallipoli Campaign. Shortly afterwards, he and his father were awarded the Nobel Prize in Physics. He was 25 years old and remains the youngest science laureate. The Problem with sound ranging was that the heavy guns boomed at too low a frequency to be detected by a microphone. After months of frustrating failure he and his group devised a hot wire air wave detector that solved the Problem. In this work he was aided by Charles Galton Darwin, william Sansome Tucker, Harold Roper Robinson and Henry Harold Hemming. British sound ranging was very effective; there was a unit in every British Army and their system was adopted by the Americans when they entered the war. For his work during the war he was awarded the Military Cross and appointed Officer of the Order of the British Empire. He was also Mentioned in Despatches on 16 June 1916, 4 January 1917 and 7 July 1919.
When demobilized he returned to crystallography at Cambridge. They had agreed that father would study organic crystals, son would investigate inorganic compounds. In 1919 when Ernest Rutherford, a long-time family friend, moved to Cambridge, Lawrence Bragg replaced him as Langworthy Professor of Physics at the Victoria University of Manchester. He recruited an excellent faculty, including former sound rangers, but he believed that his knowledge of physics was weak and he had no classroom experience. The students, many veterans, were critical and rowdy. He was deeply shaken but with family support he pulled himself together and prevailed. He and RW James measured the absolute Energy of reflected X-rays, which validated a formula derived by CG Darwin before the war. Now they could determine the number of electrons in the reflecting targets, and they were able to decipher the structures of more complicated crystals like silicates. It was still difficult: requiring repeated guessing and retrying. In the late 1920s they eased the analysis by using Fourier transforms on the data.
Bragg was elected a Fellow of the Royal Society (FRS) in 1921—"a qualification that makes other ones irrelevant". He was knighted by King George VI in the 1941 New Year Honours, and received both the Copley Medal and the Royal Medal of the Royal Society. Although Graeme Hunter, in his book on Bragg Light is a Messenger, argued that he was more a crystallographer than a Physicist, Bragg's lifelong activity showed otherwise—he was more of a Physicist than anything else. Thus, from 1939 to 1943, he served as President of the Institute of Physics, London. In the 1967 New Year Honours he was appointed Companion of Honour by Queen Elizabeth II.
In 1930 he became deeply disturbed while weighing a job offer from Imperial College, London. His family rallied around and he recovered his balance while they spent 1931 in Munich, where he did research.
He became Director of the National Physical Laboratory in Teddington in 1937, bringing some co-workers along. However, administration and committees took much of his time away from the workbench.
During the war the Cavendish offered a shortened graduate course which emphasized the electronics needed for radar. Bragg worked on the structure of metals and consulted on sonar and sound ranging, they still used the Tucker microphone. He became Sir Lawrence in 1941, happily resolving the confusion caused by father and son william Bragg. His father died in 1942, during which Bragg served for six months as Scientific Liaison Officer to Canada. He organized periodic conferences on X-ray analysis, which was widely used in military research.
In 1953 the Braggs moved into the elegant flat for the Resident Professor in the Royal Institution in London, the position his father had occupied when he died. In 1931 and 1934 Lawrence had delivered the Royal Institution Christmas Lecture and since 1938 he had been Professor of Natural Philosophy in the Institution, delivering an annual lecture. Father's successors had weakened the Institution, so Lawrence had to rebuild. He bolstered finances by enlisting corporate sponsors, The traditional Friday Evening Discourses were followed by a dinner party for the speaker and carefully-selected possible patrons, more than one hundred and twenty of them each year. "Two of these Discourses in 1965 gave him particular pleasure. On 7 May, Lady Bragg, who had been a member of the Royal Commission on Marriage and Divorce (1951-55) and was Chairman of the National Marriage Guidance Council, lectured on 'Changing patterns in marriage and divorce'; and on 15 November, Bragg listened with evident pride to the Discourse on 'Oscillations and noise in jet engines' given by his engineer-son Stephen, who was then Chief Scientist at Rolls Royce Ltd and later became Vice-Chancellor of Brunel University." He also introduced a new program of highly regarded Schools' Lectures, enlivened by the elaborate demonstrations that were a hallmark of the Institution. He gave three of these lectures on 'electricity'
He continued research in the Institution by recruiting a small group to work the Davy-Faraday Laboratory in the basement and in the adjoining house, supported by grants he obtained. A visitor to the laboratory succeeded in inserting heavy metals into the enzyme lysozyme; the structure of its crystal was solved in 1965 at the Royal Institution by D C Phillips and his coworkers, with the computations on the 9,040 reflections performed on the digital computer at the University of London, which greatly facilitated the work. Two of the illustrations of the positioning of amino acids in the chain were drawn by Bragg. Unlike myoglobin, in which nearly 80 per cent of the amino-acid residues are in the alpha-helix conformation, in lysozyme the alpha-helix content is only about 40 per cent of the amino-acid residues found in four main stretches. Other stretches are of the 310 helix, a conformation that they had proposed earlier. In this conformation, every third peptide is hydrogen-bonded back to the first peptide, thus forming a ring containing ten atoms. They had the complete structure of an enzyme in time for Bragg's seventy-fifth birthday. He became Professor Emeritus in 1966.
Among Bragg's other interests was shell collecting; his personal collection amounted to specimens from some 500 species; all personally collected from South Australia. He discovered a new species of cuttlefish – Sepia braggi, named for him by Joseph Verco.
Bragg's hobbies included drawing — family letters were illustrated with lively sketches — painting, literature and a lifelong interest in gardening. When he moved to London, he missed having a garden and so worked as a part-time gardener, unrecognized by his employer, until a guest at the house expressed surprise at seeing him there. He died at a hospital near his home at Waldringfield, Ipswich, Suffolk. He was buried in Trinity College, Cambridge; his son David is buried in the Parish of the Ascension Burial Ground in Cambridge, where Bragg's friend, who had he survived would have been his brother-in-law, Rudolph Cecil Hopkinson is also buried.