One option is to use a hash to track the lab count (using the lab numbers as keys, so they can be numerically sorted later). If the count is 2, then the lab is paired, else it's unpaired:

use strict;
use warnings;

my %hash;

while (<DATA>) {
    $hash{$1}++ if /^lab(\d+)_/;
}

for my $lab ( sort { $a <=> $b } keys %hash ) {
    print "lab$lab is ", ( $hash{$lab} == 2 ? 'paired' : 'unpaired' ),
+ "\n";
}

__DATA__
lab1_set1.txt
lab1_set2.txt
lab2_set1.txt
lab3_set1.txt
lab3_set2.txt
[download]

Output:

lab1 is paired
lab2 is unpaired
lab3 is paired
[download]

Hope this helps!