This is untested tested (see below)...

But as perlre states, "Sometimes it's still easier just to say: if (/bar/ && $` !~ /foo$/) ."

Updated: Switched m!! to m##.

Update: Here's a test. I think I captured the intent behind your question:

use strict;
use warnings;

my @strings = ( '/lawyers/stuffLDSstuff/~Firms.html',
                '/lawyers/stuffnotstuff/~Firms.html' );
                
foreach my $string ( @strings ) {
    print $string;
    if( $string =~ m#/lawyers/(?!.*LDS).*~Firms\.html# ) {
        print " matches.\n";
    } else {
        print " doesn't match.\n";
    }
}
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