The Men Who Stare at Goats/WMG

Angela Lansbury did know.
Just not the Angela Lansbury the army contacted.

The goat really did die from a psychic attack.
It's too much of a coincidence for it to drop dead at that exact moment.

Hooper's Dim Mak didn't work. Lyn just believed it did.
A recurring gag regarding Larry Hooper, is that regarding anything psychic or mystical related, he fails spectacularly. His introduction, has referenced that he is a failed Science Fiction Author. During the ESP test, he mockingly invokes a spirit guide, but still fails at guessing what's in the cabinet. When he tried to enhance Norm's psychic powers, through LSD and Hypnosis, all it did was make Norm rage out and kill himself. When Lyn's tour ended, he struck him on the bridge of the nose. Causing him to collapse. Any combatant could tell you, that even the slightest flick on the bridge of the nose could disorient and knock down the victim of said strike. This is because, when struck there, it effects the eyes and ears surrounding it, throwing them temporarily off balance.

Lyn however, is a firm believer of the technique and believed that even if it takes him a long time, he will die from it. He attributes getting cancer due to the Dim Mak. This troper guesses, that the same Psi-Energy that fuels his powers, such as Cloud Bursting and Remote Viewing; also got fuelled by his subconscious belief that Hooper marked for death. Causing his body to act accordingly. Even Lyn mentioned at one point he didn't know if the Cancer was caused by the Dim Mak or not.