Multisite - Commerce reference between sites
So I have discovered that I will need to create a Rule using the module Rules URL Argument that will take the URL /add-to-cart/[SKU] and add this to cart.

I can create a field on the main site for the SKU and this then outputs the link to the LMS website.

The source is here:
https://www.youtube.com/watch?v=6Rn7FLFytTU