That was already on the way . The reason literacy improved quickly under the Communists is that it was already improving at an accelerating rate. It takes decades to have literacy to really take off. You need enough literate adults to teach the children.Something to consider is that as bad Lenin was, he did do some basic things like created a free education system that alone was better than anything the white officers could plan.
With a low starting literacy rate that means teaching some of the children, getting them through school, having some of them become teachers so they can teach the new batch of students so some of them can become teachers and so on. That doesn't happen overnight.