regex implementation to replace group with its lowercase version

Is there any implementation of regex that allow to replace group in regex with lowercase version of it?

If your regex version supports it, you can use \L, like so in a POSIX shell:

sed -r 's/(^.*)/\L\1/'

In Perl, you can do:

$string =~ s/(some_regex)/lc($1)/ge;

The /e option causes the replacement expression to be interpreted as Perl code to be evaluated, whose return value is used as the final replacement value. lc($x) returns the lowercased version of $x. (Not sure but I assume lc() will handle international characters correctly in recent Perl versions.)

/g means match globally. Omit the g if you only want a single replacement.