You're right. Lambdas in C++ are syntactic sugar over something the core language has allowed you to do since before C++98. Since you control which variables you capture into the closure, and how, when writing the lambda, all of the information regarding how to make it (e.g. it's size, data members, etc) is static, and so it does not require the use of the heap at all. A concrete example. The following C++ examples do the same thing, and neither touch the heap:

    // A. Using a struct. The old manual way.
    struct my_lambda {
        my_lambda(int c) : c_(c) {}
        int operator() (int x) const {
            return x == c_;
        }
        int c_;
    };
    
    auto f(vector<int> numbers) {
        my_lambda lam(2);
        // remove all the matching elements
        erase_if(numbers, lam);
        return numbers;
    }

    // B. Using a lambda
    auto g(vector<int> numbers) {
        int c = 2;
        erase_if(numbers, [c](int x) { return x == c; });
        return numbers;
    }