Andreas Lauritz Clemmensen was in Leck, Duchy of Schleswig. He was the son Carl Frederik Clemmensen and Charlotte Laurence Hass, He attended C.V. Nielsens Tegneskole and was admitted to the Royal Danish Academy of Fine Arts in 1867, from which he left as an architect in 1875. During his studies he was a draftsman for Johan Daniel Herholdt and Hans J. Holm. He conducted travel studies in Italy, France, England and the Netherlands in the years 1880-83 and again in Italy 1901, 1906, 1921 and 1923. He was in Sweden in 1921.
Clemmensen was chairman of the Academic Association of Architects (Academic Arkitektforening) 1904-07, royal building inspector 1904-1911. He was the architect of Roskilde Cathedral from 1914. He exhibited drawings at Charlottenborg Spring Exhibition in 1876, 1887, 1892, 1900, 1909, 1910 and 1929. In 1916 he became Knight of the Order of the Dannebrog.
Clemmensen was married in 1884 with Dagmar Sofie Becker (1859 - 1917). He was the father of son Eigil Clemmensen (1890 – 1932) and Mogens Clemmensen (1885-1943). He died during 1928 in Copenhagen.