Parallel updates on header and line item tables in SSIS
Less of a race condition and more of an issue with order of operations and dependencies.
The way you stated your question, in steps, is how you want to think of the SSIS package.  First it has to do this, then it has to do that.
Since the line items are dependent on the latest information from the header, that should always come second.  Letting them go simultaneously, you don't really know what happens first.