Replacing std::function from within itself (by move-assignment to *this?)

Is it possible to replace one std::function from within itself with another std::function?

The following code does not compile:

#include <iostream>
#include <functional>

int main()
{
    std::function<void()> func = []()
    {
        std::cout << "a\n";
        *this = std::move([]() { std::cout << "b\n"; });
    };
    func();
    func();
    func();
}

Can it be modified to compile?
The error message right now is: 'this' was not captured for this lambda function - which I completely understand. I don't know, however, how I could capture func's this-pointer. I guess, it is not even a std::function inside the lambda, yet?! How can this be done?

Background: What I want to achieve is the following: In the first invocation of a given std::function, i would like do some initialization work and then replace the original function with an optimized one. I want to achieve this transparently for the user of my function.

The expected output of the example above is:

a
b
b