Comparator for Optional<T> with key extractor, like java.util.Comparator.comparing

You can use Comparator#comparing(Function,Comparator):

Accepts a function that extracts a sort key from a type T, and returns a Comparator<T> that compares by that sort key using the specified Comparator.

Here's an example based on the code in your question:

persons.sort(comparing(Person::getLastName, comparing(Optional::get)));

Basically this is using nested key extractors to ultimately compare the String objects representing the last names. Note this will cause a NoSuchElementException to be thrown if either Optional is empty. You can create a more complicated Comparator to handle empty Optionals¹:

// sort empty Optionals last
Comparator<Person> comp =
    comparing(
        Person::getLastName,
        comparing(opt -> opt.orElse(null), nullsLast(naturalOrder())));
persons.sort(comp);

If you need to do this a lot then consider creating utility methods in a manner similar to Comparator#nullsFirst(Comparator) and Comparator#nullsLast(Comparator)¹:

// empty first, then sort by natural order of the value
public static <T extends Comparable<? super T>> Comparator<Optional<T>> emptyFirst() {
  return emptyFirst(Comparator.naturalOrder());
}

// empty first, then sort by the value as described by the given
// Comparator, where passing 'null' means all non-empty Optionals are equal
public static <T> Comparator<Optional<T>> emptyFirst(Comparator<? super T> comparator) {
  return Comparator.comparing(opt -> opt.orElse(null), Comparator.nullsFirst(comparator));
}

// empty last, then sort by natural order of the value
public static <T extends Comparable<? super T>> Comparator<Optional<T>> emptyLast() {
  return emptyLast(Comparator.naturalOrder());
}

// empty last, then sort by the value as described by the given
// Comparator, where passing 'null' means all non-empty Optionals are equal
public static <T> Comparator<Optional<T>> emptyLast(Comparator<? super T> comparator) {
  return Comparator.comparing(opt -> opt.orElse(null), Comparator.nullsLast(comparator));
}

Which can then be used like:

persons.sort(comparing(Person::getLastName, emptyLast()));

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^{1. Example code simplified based on suggestions provided by @Holger. Take a look at the edit history to see what the code looked like before, if curious.}