I cannot pass lambda as std::function

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It’s because a lambda function is not a std::function<...>. The type of 

auto lambda = [](const std::string& s) { return std::stoi(s); };

is not std::function<int(const std::string&)>, but something unspecified which can be assigned to a std::function. Now, when you call your method, the compiler complains that the types don’t match, as conversion would mean to create a temporary which cannot bind to a non-const reference.

This is also not specific to lambda functions as the error happens when you pass a normal function. This won’t work either:

int f(std::string const&) {return 0;}

int main()
{
    std::vector<int> vec;
    C<int> c;
    c.func(vec, f);
}

You can either assign the lambda to a std::function

std::function<int(const std::string&)> lambda = [](const std::string& s) { return std::stoi(s); };

,change your member-function to take the function by value or const-reference or make the function parameter a template type. This will be slightly more efficient in case you pass a lambda or normal function pointer, but I personally like the expressive std::function type in the signature.

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

    // or
    void func(std::vector<T>& vec, std::function<T( const std::string)> const& f){
        //Do Something
    }

    // or
    template<typename F> func(std::vector<T>& vec, F f){
        //Do Something
    }
};

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