The crux of Lange's argument was that planners do not need to know more than private capitalists, as both in real life proceed through the process of trials and errors to adjust their prices. So that undercuts the supposed omniscience required in planning but not private capitalism - in fact neither requires it to improve efficiency.
Lange argued that both planning and capitalism are on equal footing in this respect. What makes planning superior is the planning ability to overcome constraints imposed by private ownership of property, which leads to either periodical crises or equilibria skewed away from optimum toward consumption of the rich. I do not think that this argument can be dismissed that easily.
As far as the price mechanisms under planning postulated by Lange - they were either not implemented or if they were, they were later circumvented by political and social mechanisms (informal economy, etc.) So as Lange aptly observed, the reasons of the central planning "failure" lie not in planning but in sociology and politics.
Alas, there is one thing that is not considered in these arguments - the capacity to externalize costs. That capacity is much greater in capitalism - under which private firms can not only dump costs on they public sector in their own countries, but also on other countries thanks to imperialism. In planning systems, the capacity for cost externalization was pretty much non-existent. First, the public ownership of the means of production meant that public sector would have to externalize to itself, which defeats the purpose. Second, the planned economies lacked the capacity to externalize on other countries because they were not imperialist (EE) or because their imperialism had strategic rather than economic nature - i.e. its goal was to maintain political influence against the west, rather than economic exploitation. In other words, while western imperialists externalized their costs on their satellites, Russian imperialists absorbed the costs of satellites to maintain their allegiance.
-- Wojtek
"An anarchist is a neoliberal without money."