Could somebody show me a quick example how to sort an ArrayList alphabetically in Java 8 using the new lambda syntax.
If you have an array with elements that have natural ordering (i.e String, int, double); then it can be achieved by: 
List myList = new ArrayList<>();
myList.add("A");
myList.add("D");
myList.add("C");
myList.add("B");
myList.sort(Comparator.comparing(s -> s));
myList.forEach(System.out::println);
 
If on the another hand you have an array of objects and you want to sort base on some sort of object field, then you can use:
class User {
    double score;
    // Constructor // Getters // Setters
}
List users = new ArrayList<>();
users.add(new User(19d));
users.add(new User(67d));
users.add(new User(50d));
users.add(new User(91d));
List sortedUsers = users
        .stream()
        .sorted(Comparator.comparing(User::getScore))
        .collect(Collectors.toList());
sortedUsers.forEach(System.out::println);
  
If the sorting is more complex, then you would have to write your own comparator and pass that in.