Many of the tools used to parse HTML use HTML::Parser under the hood, and it is worthwhile knowing how it works. This script gathers up all the content of each list item, including other elements, into a variable. When it meets the closing list item tag, you can do what you need to the content before printing it out.

use HTML::Parser;

my $inside_li = 0;
my $list_item = '';

sub start {
    my ($tag, $text) = @_;
    if ($inside_li) {
        $list_item .= $text;
        return;
    }
    if ($tag eq 'li') {
        $inside_li = 1;
    }
    print $text;
};

sub text {
    my ($text) = @_;
    if ($inside_li) {
        $list_item .= $text;
        return;
    }
    print $text;
};

sub end {
    my ($tag, $text) = @_;
    if ($tag eq 'li') {
        $inside_li = 0;
        # do things to <li> content
        $list_item =~ s/^\s+//;
        print $list_item;
        $list_item = '';
    }
    if ($inside_li) {
        $list_item .= $text;
        return;
    }
    print $text;
};

my $parser = HTML::Parser->new(
    api_version => 3,
    start_h     => [\&start, "tagname, text"],
    text_h      => [\&text,  "text"],
    end_h       => [\&end,   "tagname, text"],
    default_h   => [\&text,  "text"],
);

$parser->parse_file(\*DATA);
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