Do I get a free upgrade when I travel with Ryanair? Oh, I forgot they don't have business. And I don't fly them ;-)
Seriously, you could just try asking nicely. However, most probably that won't work. As far as I have been told by LH cabin crew, they are not allowed to upgrade anyone on board for free unless in exceptional circumstances that are justifiable. At check in or at the gate they will first try to sell all available space in business and premium economy and only then give it away to customers with status (HON Circle, Senator, Frequent Traveller or equivalent in that order) and typically only if it suits them, meaning if economy is overbooked.
Perhaps try to upgrade using miles or cash if possible?
Why is this in the biz jet section anyway?