In order for grades to be passed back to your LMS, each student has to have logged in to WeBWorK at least once using the link in the LMS for the respective assignment/course. This link provides data to WeBWorK as to how to send the grade back to the LMS.
This is a consideration when determining the value of $external_auth. If a student always logs in to WeBWorK directly (not through the LMS), then WeBWorK will be unable to send the grade for that student back to the LMS.