This is a great question and is something important to consider when planning where you want your products to feature.
When products are hosted on a Shopify online store, the platform designates individual product pages that can be indexed and featured in search engine search results. However, when you're on the Lite plan and are using the Buy Button to embed your products on a third party site, all of the indexing will come from the website/ platform that the products have been embedded into. If, for example, you wanted your Buy Button products to be indexed individually, you'd need to create specific pages on the third party platform for each product. The products themselves are not indexed directly, but rather the pages they appear on.
I hope this helps but please let me know if you have any further questions! If you're interested in learning more about improving your site's search engine optimization (SEO), feel free to check out our beginner's guide to ecommerce SEO for advice and guidance on this topic.
Victor | Shopify Social Care