This is the current set up:
I have a landing page hosted on a subdomain dedicated to landing pages (ex. lp.mysite.com/product-01 and lp.mysite.com/product-02).
Each landing page has a Buy Now button, which links to mysite.com/cart/01?discount=freeshipping with 01 being the product number.
This link redirects the visitor to the checkout page at checkout.shopify.com/{string} and adds both the product and the discount code.
It wouldn't be enough to simply set the conversion goal to be the destination path of mysite.com/cart/01?discount=freeshipping since I want to track sales, which means I need to track the user when he is redirected to the checkout page and also after they've completed payment. For Shopify, funnel tracking is done by tracking the thank you page which is shown after payment. Link
My question is: How do I properly set up Google Analytics to track conversions that start on my landing pages on a subdomain to the checkout page?