Как правильно заблокировать средство получения List в C #

I am wondering how to properly lock the getter of type List. I have one static class that looks something like this:

class FirstClass {
static private locker = new object();   
static private List<String> _my_list;

public static List<String> my_list {
    get {
        lock(locker) {
            return my_list;
        }
    }
}

private static void thread_func() {
    // do something periodicaly with the list
    // for example:

    lock(locker){
        _my_list.Add();
        _my_list.RemoveAt();
        ...
    }
}

}

Then, I have another class that looks like this:

class SecondClass {
private void thread_func() {
    foreach(string s in FirstClass.my_list) {
        // read every item in the list
    }
}

}

So, first class has a public list that the second class uses. First class periodically updates the list in one thread, and second class reads the list at an random interval on a second thread.

Does this locking mechanism ensure that the list will not be modified by the first class while the second class is reading it and vice-versa?