In "Where Have You Gone, Charming Billy?" Paul can't help but laugh over Billy Boy's death because

He feels that death in general is funnier than it is tragic.
He finds it ironic that Billy Boy died of a heart attack in a war.
He believes that Billy Boy deserved to die a more heroic death.
He knows that Billy Boy would have found it amusing to die that way

He finds it ironic that Billy Boy died of a heart attack in a war.

In "Where Have You Gone, Charming Billy?", Paul can't help but laugh over Billy Boy's death because he finds it ironic that Billy Boy died of a heart attack in a war.