I cannot pass lambda as std::function

Let's focus on this example:

template<typename T>
class C{
    public:
    void func(std::vector<T>& vec, std::function<T( const std::string)>& f){
        //Do Something
    }
};

And now, I am trying:

std::vector<int> vec;
auto lambda = [](const std::string& s) { return std::stoi(s); };
C<int> c;
c.func(vec, lambda);

It causes errors:

no matching function for call to ‘C<int>::func(std::vector<int, std::allocator<int> >&, main()::<lambda(const string&)>&)’
     ref.parse(vec, lambda);

Please explain me what is not ok and how to implement it with std::bind as well.