The user is using DataLoader to update Call Discussion records, which are associated with a submitted Call. Even if the Override_Lock_vod__c field on the Call Discussion object is set to True, the error still occurs: Error: You may not update a submitted call or any supporting data
One possible reason is that there is a Roll-Up Summary type custom field on the Call object and its Summarized Object is Call Discussion.
So, when updating Call Discussion records, the associated Call record is re-calculated and updated as well. Since the Call is submitted, it is not allowed to be updated and the error occurs.
Consider setting the Override_Lock_vod__c filed on Call object to true through the use of a workflow when Call Discussion is updated. As this is one way to correct this error, there can be other ways available based on the business requirement.