lc alone should do. You shouldn't have to use normalize, and it should work for all scripts. Make sure you've decoded the text.

If you're unlucky, you may have to use one of the following:

utf8::upgrade($s);
lc($s)
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or

use feature qw( unicode_strings );
lc($s)
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If you're still have problems, please provide a sample string. Preferably using

use Data::Dumper;
local $Data::Dumper::Useqq = 1;
print(Dumper($s));
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or

use Devel::Peek;
Dump($s);
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