I can't imagine a corporate TA contract which would provide for "day of" changes when those can't be made and effectively ticketed, but if one's employer requires that which can't be done and the TA offers a service which it can't provide, OP should still dump this back in the lap of the TA and the reimbursement in the lap of his travel people. The situation here is hardly an odd one. Moving flights by a day occurs frequently.

I don't see that this is a BA issue at all. OP no showed on a ticket and it was cancelled. This caused OP to purchase a new ticket out-of-pocket. He has been refunded the pittance of taxes payable at LUX and that is the end of it for BA.

He was misled by his TA (and perhaps his employer).