“LDF” is used for several different organizations, but the two most common are:

  • NAACP Legal Defense and Educational Fund (often just called “LDF”): established in 1940 by Thurgood Marshall as a separate legal entity from the NAACP.
  • Left Democratic Front in Kerala, India: formed as a political alliance around 1979–1980.

If you tell me which LDF you mean (civil rights law firm, Kerala political alliance, Lesotho Defence Force, etc.), I can narrow it to the exact founding date for that one.