It's pretty easy to setup the payment gateway if you're using one of the common ecommerce platforms like Shopify, Woocommerce or Magento.

I would suggest going that route first before getting deep into the APIs, too much potential for making mistakes.

Also, once you have everything setup make sure you test everything using their Litecoin Testnet (LTCT). You can request this coin with no value for free for testing purposes to see when payments come through and how they are logged/reported.

Good luck!