Hi scripps_l,
The SSO key and client Jar files are typically provided by the Lithium-appointed project manager during the launch process. If you're not yet a Lithium customer, I'd suggest contacting your sales representative to discuss further evaluating Lithium SSO.
Regarding your last question, I'm not sure I quite follow what you're asking, but it's important to keep in mind that the community must be in the same domain that you're setting the SSO cookie in order for the Lithium application to read that cookie. This is typically accomplished by adding a CNAME record that maps a subdomain (ie. community.yourdomain.com) to your Lithium community instance. If that doesn't answer your question, can you please clarify?
I hope this helps!