You can enable Printful's live shipping rates for the Venture, Business, and Unlimited plans by checking this box:
We don’t recommend using Printful's live rates with weight-based rates or other global rates in Ecwid by Lightspeed.
If you’re selling items that are not fulfilled with Printful, you will need to set up individual shipping rates for these products, since Printful live rates will not be applied.
Alternatively, you can disable Printful live rates and set up individual fixed shipping rates for Printful items.
To set up individual fixed shipping rates, go to each product's settings in Ecwid by Lightspeed → Shipping and taxes → Set up fixed rate per item. This is the price that will be charged for shipping this individual product (with or without other products in the cart).