Sorry, what's LTI?
From the page: "The IMS Learning Tools Interoperability (LTI)® specification allows Learning Management Systems (LMS) or platforms to integrate remote tools and content in a standard way."
If you haven't used an LMS ("Learning Management System") it's kinda like WordPress for teaching - teachers create course materials without needing to know HTML.
I'm not super familiar with LTI, but it looks like the company that does this also does the Common Cartridge spec (which I'm more familiar with)
To answer your question:
Let's say that I'm teaching at course at University A using the Canvas LMS. At the end of the quarter the teacher asks the LMS to "Export The Course", which produces a file in the Common Cartridge format (essentially a .ZIP file with XML manifests and any supporting files bundled along with it). Later if you wanted to copy that course into an LMS then you can upload the Common Cartridge format and it should just work (at which point you can copy the course contents, in part or in whole, to the new course).
I'm guessing the LTI is the same idea, but for the LMSs to talk to each other while they're running.
Typically LTI is used to add third party components (or in-house ones) to an LMS. For example we have our own Teams Integration, lecturers can make a Microsoft Team corresponding to any course they teach, their students can see the URL of the team if they've lost it but can't leave or create a team.