'!=' is for numbers, 'ne' is for strings, but in this case you don't need to use either as nslookup() returns undefined if it fails. Here's a little cleaned up version:

use strict;
use warnings;
use Net::Nslookup;

foreach (@ARGV) {
    my $name = nslookup(host => $_, type => "PTR");
    if ($name) {
        print("looking up ... $name ...");
        my $ipAddr = nslookup(host => $_, type => "A");
        print "$_ $name $ipAddr\n";
    }
    else {
        print("NOT looking up ... $_ ...\n");
    }    
}
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