Welcome to the Shopify Community! Loomis is not an option through the natural admin to be connected to your Shopify shipping rates at this time. Only some carriers are able to be connected directly to your Shopify store. This will depend on the country you are operating in. For example, in the US you can connect your own FedEx, UPS and USPS accounts. There is more about connecting carrier accounts in our Help Center under Third-party carrier-calculated rates.
As an alternative, if you wish to ship with Loomis, you could look into a third party shipping app that allows you to use Loomis as a carrier. These apps usually display their own discounted rates for each carrier, rather than allow you to connect your own account.
In order to connect your own shipping carrier account, or to use a third party shipping app, your store must have our carrier-calculated shipping feature enabled. There is more about this in the help document I shared above as well.
Another great option is to use Shopify Shipping if you are eligible. You can show carrier-calculated rates at checkout for USPS, DHL Express, or UPS if you're store is based in the United States. Shopify Shipping is available for stores based in the United States, Canada or Australia. There is more about Shopify Shipping eligibility on our Help Center.
Lastly, you can always use Loomis to purchase your labels and ship your orders without a connection to Shopify. In this scenario, you would not have real-time rates available for your customers at checkout, and would need to create flat shipping rates. Although perhaps not the ideal solution, this would still allow you to ship with your chosen carrier and account.
Let me know if you have any further questions!