Our previously developed analytical infinite order sudden quantum theory of triatomic photodissociation is generalized to compute fragment internal energy distributions when the initial triatomic rotational state has K not equal 0. The dependence of product rotational energy distributions on initial rotational and vibrational state is illustrated through model computations for the direct NOCl photodissociation from the ground to the T-1(1 (3)A") potential energy surface. The calculations consider all J,K less than or equal to 9 and employ a repulsive potential that is fit to ab initio computations. Comparisons of fragment rotational distributions with previous semiclassical approximations further elucidate the role of the mapping of the initial state bending wave function onto the fragment rotational distributions and the influence of parent rotations on this mapping. The infinite order sudden quantum-mechanical distributions exhibit a more complex structure, but upon thermal averaging they are already transformed at T=3 K into fairly broad rotational distributions. The present theory readily permits the calculations of energy distributions for initial states of high J and K.