when our customers come with such a request, i always suggest to create some sort of business (enrolment) rules engine within your HRM/management tool and use enrolment API to assign students to courses based on their roles.
LDAP can be used as SSO, but that's it - no groups support, etc. The best you can do is distinguishing staff/students.
as for the LTI - if i got you correctly, then no - you can't add new courses to Open edX, but you can add a module to the course (in Studio) which will render some 3rd party content served via LTI. And no, you can't "enroll" students to a course via LTI.