Why are you trying to numerically sort stuff that you feel you have to lowercase first? I would strongly recommend that you rewrite your sort as a Schwartzian Transform. Something along the lines of:

@lines =
    map {
        $_->[1],
    } sort {
        $b->[0] <=> $a->[0]
    } map {
        [ SORTBY_VALUE_HERE, $_ ]
    } @lines;
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So, you would put your algorithm for determining the SORTBY_VALUE in the lower map-statement. This is not only more efficient, but it's also more descriptive of what you're actually trying to do. Your solution has the look of a bunch of cancerous tumors that have grown one atop the other. You're closing your eyes and stabbing at a solution. The amazing thing is how far you've gotten.