Airbus A-310 autopilot on climb

I don’t think so. The MCDU is quite simplistic really. There’s not that much that you can program in it, compared to more modern Airbusses and Boeings.

And as far as I know, LVL CHG should hold whatever speed you dial in into the autopilot panel. So let’s say you set your autopilot speed to 220 knots and you turn on your LVL CHG, than the aircraft should ascend or descend based on the 220 knots.