Hi Vinod,
I presume that your question is about what happens to LTI Links to external learning tools when you copy the content from one course to another? I also presume that the "context" you're talking about is the LTI property "context_id"?
Note that the context_id always describes the context from which the LTI Launch happens at launch time. It is not settable at link placement time, and it contains the context for the launch, and not any historical context.
Also, you cannot, through LTI, determine the course from which the current context was copied.
If the way you're copying is from a Course Template org unit to a Course Offering org unit, and the Course Template is a parent of the Course Offering in the D2L Learning Environment org unit structure, then that structural information
is available through Valence Learning Framework APIs. A calling user with sufficient privileges can use the org structure APIs (
http://docs.valence.desire2learn.com/res/orgunit.html) to retrieve property details about org units, including their position in the course hierarchy. Note that, typically, the kinds of users that are initiating LTI launches (instructors and students) may not, themselves, have sufficient permissions based on their LMS role to use these APIs: they're more intended for use by administrator role users.
Also, if you're copying Course A to Course B, and you're not linking them together explicitly in the org unit structure, there's really no way to keep track of that copy operation after the fact, through the API. The "source" of an org unit's initial properties/data is not maintained as a property: only the org unit's structural relationship within the hierarchy is (which you could lean on, if the rules around when copying happens in your organization are directly tied to the org unit structure).