You can upgrade with avios if you are in an eligible fare class and there are award seats available, however this cannot be done if you are checked in or done by airport staff. If you are checked in you would need to be offloaded from the flight. If you are booked in a discount economy fare you can't upgrade with avios.
You can ask about discount cash upgrade offers at the airport (AUP). Either at the checkin desk or sales desk. This may also be offered through MMB at anytime or at OLCI (POUG).
There is no facility to upgrade on boarding or at the gate (other than op-up).