Hi Hari,
Yes, the process should be the same to change your Legacy Source System definition from Legacy Production to Legacy QA as you did for your ECC and CRM system.
Are you sure your Legacy QA has all the same tables and views as in Legacy Prod?
It would not surprise me if custom views were created to support BW in Legacy Prod , but never applied (or updated) to Legacy QA.
Good luck,
John Hawk