A) simple is beautiful :)

B) arbitrary input where performance matters ? This won't have any meaningful substrings other than ""

Maybe of interest:

I tried to beat sort, where much of the result is useless, cause we only need the first and last element and nothing in between.

The results are not too spectacular, though its requires less memory:

 
use warnings;
use strict;
use Time::HiRes qw/time/;

my $common = join "","a".."z";

my @x = map { $common . rand 1 } 1..1e6;
my (@a,$a,$b,$start);

print "\n--- with full sort\n";
@a=@x;

$start=time();
my @b= sort @a;

print $b[0],"\n",$b[-1],"\n";
print time -$start,"\n";


print "\n--- with triple sort\n";
@a=@x;

$start=time();
$a= shift @a;
$b= shift @a;



($a,undef,$b) = sort($a,$_,$b) for  @a;


print $a,"\n",$b,"\n";
print time -$start,"\n";

print "\n--- with assignment\n";
@a=@x;
$start=time();
$a= shift @a;
$b= shift @a;

for my $x (@a) {
    $a = ($x,$x,$a)[$a cmp $x];
    #next if $a eq $x;
    $b = ($x,$b,$x)[$b cmp $x];
}

print $a,"\n",$b,"\n";
print time -$start,"\n";


print "\n--- with goto\n";

@a=@x;

$start=time();

$a= shift @a;
$b= shift @a;

for my $x (@a) {
    goto ("NEXT", "NEWMIN", "MAYBEMAX")[$a cmp $x];
  NEWMIN:
    $a=$x;
    next;
  MAYBEMAX:
    goto ("NEXT", "NEXT",   "NEWMAX"  )[$b cmp $x];
  NEWMAX:
    $b=$x;
  NEXT:
}

print $a,"\n",$b,"\n";
print time -$start,"\n";
[download]

output:

--- with full sort
abcdefghijklmnopqrstuvwxyz0.000100396248079448
abcdefghijklmnopqrstuvwxyz9.99150346814304e-06
7.66956496238708

--- with triple sort
abcdefghijklmnopqrstuvwxyz0.000100396248079448
abcdefghijklmnopqrstuvwxyz9.99150346814304e-06
5.88848209381104

--- with assignment
abcdefghijklmnopqrstuvwxyz0.000100396248079448
abcdefghijklmnopqrstuvwxyz9.99150346814304e-06
1.2906858921051

--- with goto
abcdefghijklmnopqrstuvwxyz0.000100396248079448
abcdefghijklmnopqrstuvwxyz9.99150346814304e-06
2.99558115005493
[download]

update

either I'm working too hard or Alzheimer is knocking at the door.

I completely forgot about le and ge and spend too much effort into emulation

print "\n--- with le/ge\n";
@a=@x;
$start=time();
$a= shift @a;
$b= shift @a;

for my $x (@a) {
    $a = $x  if  $a ge $x;
    $b = $x  if  $b le $x;
}

print $a,"\n",$b,"\n";
print time -$start,"\n";
__END__
--- with le/ge
abcdefghijklmnopqrstuvwxyz0.000100420329498974
abcdefghijklmnopqrstuvwxyz9.95282924378671e-05
0.773550033569336
[download]

your version is of course faster

   DB<129> push @a, join "",a..z,rand(1) for 1..1e6
 => ""

  DB<130> $start=time;print lcp_v4(@a);time -$start
 => 1.25800704956055
abcdefghijklmnopqrstuvwxyz
  DB<131> $start=time;print lcp_v5(@a);time -$start
 => 6.93630909919739
abcdefghijklmnopqrstuvwxyz
[download]

> # however, these assume strings don't end with \0

See thats the benefit of a simple algorithm, sort doesn't care about \0, one could easily replace the comparison of 2 lines with something stable without notable impact.

I could call using modules cheating, but

a) it's core

b) you have to admit that hippo's sort approach is sexy!

--- with le/ge 
abcdefghijklmnopqrstuvwxyz0.000100071512918021
abcdefghijklmnopqrstuvwxyz9.83499014282074e-05
0.786839962005615

--- with minstr/maxstr 
abcdefghijklmnopqrstuvwxyz0.000100071512918021
abcdefghijklmnopqrstuvwxyz9.83499014282074e-05
0.23346209526062
[download]

Though your final comparison fails with some edge cases :-P