Georges Jorisch says Gustav Klimt's 1906 oil on canvas painting - called Blooming Meadow and worth up to £10m - belonged to his Jewish grandmother, Amalie Redlich, before she was sent to her death in Poland.
Mr Lauder, the chairman of Estee Lauder Companies, bought the painting in 1983 from Serge Sabarsky, an Austrian-born art dealer. It currently hangs in his New York apartment. Yesterday, 79-year-old Mr Jorisch, who escaped the holocaust by fleeing with his father to Belgium, launched a legal bid in Manhattan to recover the painting or receive its value in compensation.
In the lawsuit he claims Blooming Meadow was first acquired by his grandmother's brother, Viktor Zuckerkandl, a Viennese steel tycoon and a friend of Klimt. He left it to Redlich when he died in 1926, and she hung it in her villa near Vienna, Mr Jorisch says.
Mr Jorisch also claims that Alfred Weidinger, the chief curator of the Austrian Gallery of Vienna, had concluded in a new published catalogue that the painting was once owned by Redlich.
However the Art Newspaper said it was not clear what evidence Mr Weidinger had used. "Jorisch recently demanded return of the Klimt painting from Lauder, but Lauder ignored the demand and refused to return the painting," the legal papers say.
Last month, the New York Times reported that 74-year-old Mr Lauder rejected Jorisch's claim and says the painting never belonged to his grandmother. A spokeswoman for Estee Lauder said Mr Lauder had no comment.
Redlich is believed to have placed her paintings in storage in 1939, two years before she was deported to Lodz, where she died. Her son sought to recover her property in 1947, but discovered it had been looted.
Mr Jorisch said he believed the painting appeared to have been smuggled out of Austria without an export permit.