I believe the shipping mode should just depend on Location, and not SKU. Hence, you do not need to lookup the SKU. Your formula should be: 'SYS07 Distribution Center Details'.Default Shipping[Lookup: 'SYS08 SKU Details'.Supplied By]
This should have been my first response, rather than looking at pre-requisites to get the formula working : )
The line item SYS08 SKU Details.Code or SYS08 SKU Details.Supplied By or both are not LIST formatted, which is a necessity for being able to lookup. Once you change it to LIST, it should work fine. Currently, I suspect at least the Code is text formatted.
Sorry if I was not clear. Updated my response below:
Before changing the format, a few pre-requisites:
1. Ensure, this line item (SYS08 SKU Details.Code) is not referenced anywhere in the model
2. If it is referenced (the system will not allow you to change the format, as it is linked in other calculations), it is better to create a new line item which is list formatted and then use it for lookup
3. If it is not referenced, you can delete the current formula, change the format, and then write a new formula which gives you list formatted result