Python code for handling HTTP cookies
Since you are not showing a whole lot of the class itself, there is not to much fundamental to be done on the presented code.

Documentation

First, you should add documentation to your class and to its methods. Use the """...""" to write those docstrings as recommended in the official Style Guide.

Style

The Style Guide also has a section on variable naming (snake_case is recommended). You're mostly following this convention, and that's also the reason why Cookies as variable name almost immediately caught my attention while first screening the code. The widely accepted convention is to only use names with the first letter capitalized for class names.

Looping

While I was at it, the following piece of code caught my attention next.

Cookies = []
for hosti in range(len(hosts)):
    if hosts[hosti] in self.jar._cookies:
        Cookies.extend(self.jar._cookies_for_domain(hosts[hosti], w_r))


Since hosts is a list, and you're not trying to do anything fancy on the elements themselves, this can be simplified to

cookies = []
for host in hosts:
    if host in self.jar._cookies:
        cookies.extend(self.jar._cookies_for_domain(host, w_r))


which I find easier to read.

String formatting

This snippet comes a little bit earlier in the code: l_req_host = "%s%s" % (req_host, '.local'). It uses the old-old Python string formatting using %. Since you specifically tagged your question as Python 3, I strongly recommend to make use of the new f-string synthax which allows you to write that same line as l_req_host = f"{req_host}.local". Here is a nice blog post talking about all the different ways of string formatting in Python and their pros and cons.

if statements

Next up on my list would be if w_r.has_header("Cookie") == False. In general there is no need to do if sth == True or if sth == False in Python. Both can be conveniently expressed as if sth or if not sth. Usually this will also allow someone to read the expression almost as if it was text. If that doesn't work, maybe think about the name of your bool variable.

Minor tweaks

At the moment the last thing I could come up with was to change self.processed = self.processed + 1 to self.processed += + 1 which saves you a few characters of typing in the future.