If at all possible I would try to go through the combinations of items once at the beginning of the script, taking the process out of the while ( <$fh> ) { ... } loop, building a single regex to match any wanted line. Something like

my @items = ();
foreach my $subset ( keys %lookingFor )
{
    foreach my $item ( @$subset )
    {
        push @items, $item;
    }
}
my $rxMatchItems;
{
    local $" = q{|};
    $rxMatchItems = qr{(?:@items)};
}
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As others have pointed out, open the output file once at the beginning of the script then the remainder of the code could be reduced to something like

while ( <$fh> )
{
    next unless m{$rxMatchItems};
    print $writeFh $_;
}
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This approach all depends on whether your items can easily be combined into one regex, but I think it might be more efficient if feasible.

I hope this is of use.

Cheers,

JohnGG