Here's two creative ways - slurp the whole file, then use regex lookahead to get the "next" line, or use tell() and seek() to read ahead then reset the current file position.

#!/usr/bin/perl

use strict; # https://perlmonks.org/?node_id=11135401
use warnings;

open my $fh, '<', \<<END or die;
line one
line two
line three
line four
line five
END

{
local $/;
local $_ = <$fh>;
while( /^(.*)\n(?=(.*))/gm )
  {
  print "$1 -> $2\n";
  }
}

print "\n";
seek $fh, 0, 0; # reset for different example

while( <$fh> )
  {
  chomp;
  my $pos = tell $fh;
  print"$_ -> ", (<$fh> // "AT LAST LINE\n");
  seek $fh, $pos, 0;
  }
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Outputs:

line one -> line two
line two -> line three
line three -> line four
line four -> line five
line five -> 

line one -> line two
line two -> line three
line three -> line four
line four -> line five
line five -> AT LAST LINE
[download]