According to me, the simplest way is to abstract the operation of "reading a chunk of data" in a procedure, like in this example:

use strict;
use warnings;

while ( my @s = read_chunk() )
{
    print join " | ", @s;
    print "\n";
}

sub read_chunk
{
    my @stuff = ();
    while( my $line = <DATA> ) {
        chomp $line;
        push @stuff, $line;
        last if $. % 4 == 0;
    }
    return @stuff;
}

__DATA__
first1
second1
third1
fourth1
first2
second2
third2
fourth2
first3
second3
[download]

So you can treat a read_chunk() operation as an atomic one.

A more clever option you could explore is using Tie::File, which allows you to manipulate the file as an array of lines, even if simgle lines are actually read only when they're needed (details on the documentation).