Livestock Grazing Indemnification Act - Provides that whenever a valid permit for livestock grazing on public grazing land is canceled on or after the date of the enactment of this Act, by the United States in whole or in part, or the right of grazing livestock thereunder is suspended in order to devote the lands covered by the permit to another public purpose including disposal, the permittee shall be compensated by the United States, in an amount determined by the Secretary of the Interior, for the losses suffered by such permittee as a result of the cancellation in whole or in part of such permit or the suspension of the right of grazing livestock thereunder.