Lindenau was born in Altenburg, where he also died. In 1830 he was the Minister of the Interior during a turbulent period in the history of Saxony. Late in the year he oversaw measures to calm violent protests demanding political reform.
He created a collection of Italian artwork from the 14th and 15th centuries by Florentine painters in an effort to create artistic awareness. He gave his art collection to the city of Altenburg on the condition that they create a museum to display the pieces. This museum was finished in 1875, and became the Lindenau-Museum.
Lindenau edited the Monatliche Correspondenz zur Beförderung der Erd- und Himmels-Kunde starting in 1807. The Journal was founded by Franz Xaver von Zach in 1800 and existed until 1813.