LateShipment.com’s Delivery Experience Management (DEM) is a real-time parcel tracking solution on the cloud. It offers complete visibility into your shipments across carriers in real-time, highlights those orders that require your attention. We offer a variety of setup options to pull in the same data. One of these steps should do. This step is crucial because it allows you to view your orders directly on your LateShipment.com account.

• Through one of the applications with which we're integrated: Shopify, Magento, WooCommerce, BigCommerce, Zoho Inventory, etc.

• Order Management Platforms

• Carrier Account real-time tracking sources

• Integration by FTP

• Integration by API 

You'll find all the info in these articles : 

Shipment Data Source Integrations
 

Note: Limitations of carrier integrations
If you choose to connect your carrier accounts as a data source, only tracking numbers would get populated and no order-related reference would be available.