I have the same issue. It seems a lookup column does not work in GroupBy function to group records. Doesn't it?
a) If so, why this is not explicitly stated when describing Lookup Columns that ... if you use it across normalized tables to connect them, then later it won't allow grouping records (for example, grouping invoice items by invoices, invoices by customers, customers by projects, etc.)
b) Is there any workaround for this (before Microsoft fixes it if does it all)?