Thread safe parallel list computation using RcppParallel

Question

I'm attempting to write code in C++ that loops over an Rcpp::List of IntegerVectors. The computation itself is complicated to explain, but for the sake of example let's suppose that I wanted to take the sum of sums of each IntegerVector (ignoring the fact that I could concatenate this list into one IntegerVector). This could be achieved by the following code:

int sumIntegerVector(const Rcpp::IntegerVector vec) {
  int sum = 0;
  for (int i = 0; i < vec.length(); i++) {
    sum += vec[i];
  }
  return sum;
}

int sumList(const Rcpp::List l){

  int sum = 0;
  for (int j = 0; j < l.length(); j++) {
    sum += sumIntegerVector(l[j]);
  }
  return sum;

}

Now, I would like to make this computation thread safe, so that I could parallelize over the loop in the sumList function (and not the sumIntegerVector function). Is there any thread safe way of doing this? I'm aware that Rcpp has a template RVector for thread safety. However, because I am looping over a list, it doesn't seem like the RVector template would be sufficient. Is there an RList template or something equivalent? Otherwise, could someone suggest a workaround?

Thanks!