Suppose you have course material in three courses on the same site, maintained by three different people in three different departments or at three different locations around the country, and each of them would like to include some activity from the other two courses into their own course, while not being responsible for the maintenance of the included material.
Can all three publish their course or those activities that are to be reused with Publish as LTI, and then the other two can add an External tool activity to their courses to include the external material, or is it required to be located at another site?
It can be done via LTI, but users will need to log out after using the shared tool and there may be unforseen problems. This is because the way the Publish as LTI tool works is by creating accounts based on the information given from LTI. And logging into that account automatically. There is an issue about improving this to use existing accounts when a moodle site includes its own tool. But that's out of scope of the LTI specification. So it may not be coming soon. Here is the issue, please vote and watch and comment on it if you can https://tracker.moodle.org/browse/MDL-57345
In the mean time, you may find it easier to create a course with course meta enrolment so that users from all three courses can access it. And then linking using the URL resource.