I have paid cash for a business class seat LIS-DXB-BNE. I want to upgrade using cash to fly the DXB-BNE leg first class. The LIS-DXB leg is not in suites, and there is no lounge in Lisbon, so I don't think it's worthwhile to upgrade that leg.

I've rung my local office, who claim that I can't upgrade only one half of the ticket using cash, I can only use FF miles (which I don't have any of).

Does that seem right? Why would Emirates say no to real money, but yes to miles?