The latter solution itches me because you're doing the test for each row, even after you switched. Note it will also fail if there's no name starting with an L in the output.

I'd do something like:

while (my $row = $dbh -> fetchrow_arrayref) {
    if ($row -> [$last_name_col] =~ /^[L-Z]/) {
        push @L_Z => $row;
        while (my $row = $dbh -> fetch_arrayref) {
            push @L_Z => $row;
        }
        last;
    }
    push @A_K => $row;
}
[download]