Ludwig Baldass studied art history at the universities of Graz, Halle, Munich and Vienna and was awarded a doctorate from the University of Vienna in 1911. He was regarded as an expert in Dutch and Gothic painting and worked initially as an unpaid intern and then from November 1912 as an assistant in the Picture Gallery at the Kunsthistorisches Museum in Vienna. After he had written an expert opinion in which he judged a forgery to be a genuine picture, he appeared as a witness in 1924 at a trial before the Vienna Landesgericht (provincial court) at which the art dealers Philipp Überall and Johann Markytan, who had commissioned the appraisal, were sentenced to several months' imprisonment. Baldass habilitated in 1926, became a lecturer in art history at the University of Vienna and was awarded the title extraordinary professor in 1934. He catalogued the paintings in Albert Figdor's collection and was given the picture Christ Before Caiaphas as a reward, which he donated in 1930 to the Picture Gallery at the Kunsthistorisches Museum. Today it is held by the Österreichische Galerie Belvedere. Just a few days after the annexation on 16 March 1938, Fritz Dworschak, provisional director of the Kunsthistorisches Museum, appointed him as provisional head of the Picture Gallery to replace Alfred Stix, who was advised to retire. On 22 April 1938, however, the Ministry of Internal and Cultural Affairs issued a decree stripping him of his venia legendi because of supposed contacts with the "Jewish art trade". His application in early summer 1938 to join the NSDAP was also rejected by the Kreisgericht (local court) in Vienna in January 1940 on the grounds that he was "unsuitable as a Party member because of his earlier tainted transactions with Jewish art dealers". Baldass was involved in the salvaging of art and cultural objects from Viennese museums. In September 1939 he examined the pictures held at the Zentraldepot, which were stored in the former Rothschild hunting lodge in Steinbach near Göstling. On the instructions of the Ministry of Internal and Cultural Affairs, he was replaced by Bruno Grimschitz in December 1939 as head of the Picture Gallery but continued to work there as a curator. In November 1940 he applied unsuccessfully to be transferred to the Graphische Sammlung Albertina, as he felt that he had not been consulted in the appraisal of the picture Man Reading, falsely ascribed to Vermeer, which was acquired by Reichsstatthalter Baldur von Schirach from the art dealer Alois Miedl. Baldass, who had also been head of the restoration department of the Picture Gallery since 1921 and was replaced in March 1943 by Gert Adriani, insisted on an "official inquiry" into the matter, as he believed that the failure to consult him disqualified him for office. The Reichsstatthalterei rejected his claim. During the Nazi era he sold the painting Half-Length Portrait of an Old Man Smoking by Hans Canon, thought to have come originally from a private collection, to the "Sonderauftrag Linz". The picture is listed in the Linz database of the Deutsches Historisches Museum as Alter Mann im Schlafrock mit Zipfelmütze und langer Pfeife (Old Man in Dressing Gown with Pointed Hat and Long Pipe). It was one of the pictures stolen in the last days of the war from the "Führerbau" in Munich and regarded thereafter as lost.
After the Second World War, Baldass became head of the Picture Gallery again. At its meeting of 9 February 1946, the Ministerkomitee für Denazifizierung der leitenden Stellen des Öffentlichen Dienstes (Ministerial Committee for Denazification of Higher Public Servants) postponed a decision on Baldass because of imprecise or incomplete details in his questionnaire. It then asked the management of the Kunsthistorisches Museum to obtain an affidavit describing his relationship to the NSDAP. In his reply, referring to the loss of the venia legendi and dismissal as head of the Picture Gallery and the restoration department, Baldass stated that he had applied to join the Party but had never received confirmation as an applicant for membership or indeed as a member. In 1947 he requested the instigation of disciplinary proceedings against himself as he had discovered that he had been accused during the Nazi era of "tainted transactions with Jewish art dealers". As no relevant indications could be found by the museum management, however, the proceedings were dropped. Baldass was appointed director in December 1948 but requested early retirement in February 1949 on health grounds. Baldassgasse in the 21st district was named after him in 1973, ten years after his death.