Leopold Richard Baur grew up in a Moravian settlement and was trained as a pharmacist. He emigrated to the Cape of Good Hope in 1847, where he worked at the pharmacy of C.F. Juritz*. He requested to be allowed to practice as a chemist and druggist that same year. His interest in botany led to an acquaintance with Carl Zeyher*, Dr. Pappe*, and C.F. Ecklon* and in March 1851 he joined Juritz and Zeyher in taking the visiting German botanist Dr. B.C. Seemann* on a botanical excursion on Table Mountain. In 1855 Baur decided to become a Moravian missionary. He learned the Xhosa language and worked at the mission stations of Enon (then in the Uitenhage district; 1855-1856), and Silo (or Shiloh, 1856-1862) in the Queenstown district. He presented his collection of Cape plants to Dr. R.F. Roser of Genadendal, who later took it to Germany.
In 1863 Baur started a new mission station at Baziya in the Transkei, where he worked until 1875. In 1873 he was visited there by the Port Elizabeth naturalist Russell Hallack*, who motivated him to resume his plant collecting. Baur sent his plants (including fungi) to P. MacOwan*, then at Gill College in Somerset East, with duplicates to the herbarium of the Royal Botanical Gardens at Kew. In the preface to Volume 6 (1897) of the Flora Capensis the editor, W.T. Thiselton-Dyer*, thanked him for this interesting collection, which was formed chiefly in the neighbourhood of Baziya. His material included a number of new species from what was then a botanically little-known area. Among others the species Disa baurii, Hesperantha baurii, Hypoxis baurii, Albuca bauri, and Scilla baurii were named after him.
In 1875 Baur was transferred back to Silo and worked in the Queenstown district untill his death. In addition to the Transkei he also collected plants in the areas around Maclear, Katberg, Mamre, Wodehouse, and Indwe.