Bearfoil,
I'm not an Airbus Pro and I'm at work without my references. I just read the system law descriptions and apply them in a particular context. The following is based on recollection, and may not be exactly accurate.
As I understand it, load protection is sensed by an accelerometer which would not be affected by the loss of airspeed information. Load protection would come from biasing the elevator control signals to relieve the g load and would be available in all but mechanical law. In Alternate Law, AOA protection reverts to an airspeed basis (instead of the angle of attack sensor) so that is why loss of reliable airspeed indications causes loss of AOA protection.
With regard to the lateral protections-I will defer to the input of others for the moment. I don't feel I understand that part of the system well enough to speak to it.
Machinbird