Landsberg was born in 1869 in Rybnik. After passing the Abitur in 1887 in Ostrowo, he moved to Berlin to study law. In 1895, having passed the First (1890) and Second State Examination (1895), he opened a lawyer's office in Magdeburg. In the beginning of 1924, he moved it to Berlin, pleading the case for Friedrich Ebert in one of his defamation suits surrounding the Dolchstosslegende in 1925.
Having joined the SPD in 1890, Landsberg was elected to the Reichstag for Magdeburg from 1912 to 1918. In 1919 and 1920, he was a member of the Weimar National Assembly. In this time, he was a member of the Council of the People's Deputies, being responsible for the press, arts and literature. In 1919, he was a member of the Cabinet Scheidemann as Minister of Justice.
After the dissolution of the Cabinet Scheidemann, Landsberg was ambassador of Germany in Belgium from 1920 to 1923. He served a second term as deputy to the Reichstag from 1924 to 1933.