She had previously recorded a world record jump of 5ft 3in, having been on the German team for two years.
But, fearing a US boycott of the 1936 Olympics in Germany, the Nazi government invited her back to try out for the German team.
Two weeks before the games began, she received a letter telling her she has not qualified to be part of the Olympic team, despite setting the world record just one month previously.
Her replacement at the Olympics was Dora Ratjen, who was later revealed to be a man.
Mrs Lambert went on to become the American champion in women's high jump in 1937 and 1938 but gave up athletics when war broke out in 1939.
She married German refugee Dr Bruno Lambert in 1938, who died in 2013.
Mrs Lambert, who has sports stadiums named after her in Queens, Berlin and her hometown of Laupheim, is survived by two children, two grandchildren, and a great-grandchild.
