Yes. Though this question is not Django specific.
Usually web servers have option to export SSL client-side certificate data as environment variables or HTTP headers. I have done this myself with Apache (not Lighttpd).
This is how I did it
On Apache, export SSL certificate data to environment variables
Then, add a new HTTP request headers containing these environment variables
Read headers in Python code
http://redmine.lighttpd.net/projects/1/wiki/Docs_SSL
Looks like the option name is ssl.verifyclient.exportcert
.
Though I am not sure how to do step 2 with lighttpd, as I have little experience on it.