I am not aware of a specific prediction by Marx or Lenin on productivity gains expected although Marxists were confident there would be great gains for several reasons. They expected a reduction in wastes caused by competition (advertising, etc) and other capitalist features such as recessions, downturns, and crises, and they expected the workers' state to efficiently organize, produce, supply, and distribute - instead of a few privately hoarding profit, revenues would be reinvested - keeping cost and price low - or shared as common wealth. Another great productivity gain would come as workers choose to work harder because they are no longer working for an exploitative boss but for a society which values them - work becomes "life's prime want" - it becomes a joy.

If anyone can find an estimate of the expected productivity gains, please share it!