In order to avoid having your HTML formatted Product Descriptions overwritten in Shopify, be sure that Update Description is Off in Channels Settings. Update Description is set to Off by Default.
This field in Shopify is mapped to the Web Long Description in LightSpeed. When a Product is created in Shopify, the Web Long Description will be uploaded to the Shopify Product Description. With Update Description set to Off, you will be able to then Edit the Description in Shopify without worry.
The Web Long Description in LightSpeed can not have any special formatting. If you wish to have nicely formatted descriptions in Shopify be sure to leave the Update Description Off and manually edit the descriptions on Shopify.