It's easy, just sort them by surname:

@sorted = sort { surname($a) cmp surname($b) } @lines;
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The surname() function (something you have to write) just extracts the surname from a line. One straight-forward solution is:

sub surname {
  my $line = shift;
  my @fields = split(/\|/, $line);
  my $fullname = $fields[1]; # extract full name
  my ($first, $last) = split(/ /, $fullname);
  return $last;
}
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I.e. split the line on vertical bars, get the full name, split the full name on spaces and return the second element.

There are more clever and efficient ways to write the surname() function, but I just want to demonstrate that you don't have to try to be clever to solve the problem.

This approach extends to any sorting by any property. Just write a function to extract (or compute) that property from the things you are sorting.

If you are concerned about efficiency, have a look at this write-up: A Fresh Look at Efficient Perl Sorting where topics such as the Orcish Maneuver, Schwartzian Transform, and packed-default sort are discussed.