"Legal experts say that Mr. Hasan could challenge the government’s decision to livestream his execution, perhaps by asserting..."

"... that a public broadcast would violate prohibitions on cruel and unusual punishment in the Uniform Code of Military Justice and the Eighth Amendment of the Constitution. Courts have rejected requests from private companies that sought to broadcast executions to the public. In 2001, a federal judge refused to allow an internet company to carry a live feed of the execution of the Oklahoma City bomber Timothy McVeigh, citing Federal Bureau of Prisons rules that forbid recording or broadcasting executions.... But the Supreme Court has not weighed in directly on the question of whether public executions are legal, particularly when requested by the government, experts said. Public executions have been seen, including by United Nations officials, as a violation of international human rights protections under the International Covenant on Civil and Political Rights...."

From "Fort Hood Shooter’s Execution Could Face Challenge in Federal Courts/Legal experts say the former Army officer convicted in a 2009 mass shooting could face a narrow, rushed path to appeal a public execution by firing squad" (NYT).