All invoices created by Channels will show an "Owing" status. The Lightspeed Onsite API does not provide access to Payments, so the payment information is saved in the Printed Notes of the Invoice. This owing status makes it easier to track orders that are waiting to be fulfilled in the Smart Finds.
Depending on your integration, a "Shopify" or "Magento" Payment Method should have been created during the setup process. Once the order is packed, apply the payment method to the Invoice. This will remove the Invoice from the Open Order Smartfind and trigger the Auto-fulfillment feature if enabled. It also helps to easily identify Ecommerce Orders on reports.
Payment Method Example