cmp_deeply may be recursive, but lc isn't. I haven't used Test::Deeply enough to know if cmp_deeply has the ability to accept a comparator callback. If it could, that would make the solution pretty straightforward, but if it can, the documentation doesn't make it apparent. ...something like this would be great:

my $result = cmp_deeply(
    $expected,
    $actual,
    sub { lc shift eq lc shift },
    "This is a test using a callback to compare.
);
[download]