I'm working to integrate my Sitecore 9.1.1 instance with a third-party service (an LMS) that uses SAML SSO. This is a one-way integration, where the front-end user logs into the site with the usual membership/roles system, and it then needs to log into the third-party service with SAML.
I've written some prior code for federated authentication, but that was for users logging into the Sitecore site, not for logging into another service. I don't know if the identity server comes into play here, but it doesn't appear to for the front-end, where I just use the standard Login method for signing people in.
What is the appropriate methodology here? Is it to call some API on the service's side to "shake hands" and sign in, passing the appropriate username and some token? Or do I need to generate some SAML package when the user logs into my site that's available when they click a link to take them to the service?