In Lightspeed, each child product of an Item-Matrix has attributes (e.g. blue, large). When you modify an attribute name in Lightspeed or even delete it and recreate, Lightspeed assigns a new internal ID to the attribute.
Shopify also has internal ID's for its attributes.
The Hyperspace integration connects the attribute internal id in 1 system to the attribute internal id in the other system.
If you rename the attribute in Lightspeed, this does not modify the existing attribute. It basically creates a new one with a new internal id.
Hyperspace contains a setting that will prevent Hyperspace from updating the attribute value if Enabled.
This will allow you to modify the attribute value directly in Shopify, but keep the attribute value the same in Lightspeed. This enables you to change an attribute value in Shopify directly.
Please note that following:
Duplicate variant values will break the product sync. For example, you have a variant of 'BLK' in Lightspeed and edit it to be 'Black' in Shopify. A few days later you create a new 'Black' variant in Lightspeed. This change now matches the change you made is Shopify.
If this occurs, the Item-Matrix won't sync new items anymore (any new items regardless of the variant value will not sync). You will need to change the 'Black' variant in Lightspeed to not match an already existing variant value in Shopify. If you change the variant from 'Black' to 'Blck' in Lightspeed, the new items in the Item-Matrix will sync and fix the issue.
In short, be careful when using this feature and avoid creating new attribute values in Lightspeed that match your modified attribute value for the same product in Shopify.