您的代码不会停止程序。
一种实现方法是在while循环中测试布尔值而不是true，当用户输入LIST时，可以将布尔值设置为false，这里我添加了这样一个变量，并将其命名为shouldEnd。

import java.util.Scanner;
import java.util.TreeSet;

public class test {
   public static void main(String[] args) {
      Scanner scanner = new Scanner(System.in);
      String email = scanner.nextLine();
      TreeSet<String> addres = new TreeSet<>();
      boolean shouldEnd = false;
      while (!shouldEnd) {
         addres.add(email);
            
         if (email.equals("LIST")) {
            for (String i : addres) {
               System.out.println(i);
            }
            shouldEnd = true;
         }
      }
   }
}

use:

import java.util.Scanner;
import java.util.TreeSet;

public class test {
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        String email = scanner.nextLine();
        TreeSet<String> address = new TreeSet<>();
        while (true) {

            address.add(email);

            if (email.equals("LIST")) {
                for (String i : address) {
                    System.out.println(i);

                    // This is the reason that the program would get terminated 
                    // instantly if you wouldn't take user input.
                    String tempstr = scanner.next();
                    exit();
                }
            }
        }
    }
}

此改进使用exit()方法终止Java程序。