No.
Refer also the oneworld rules:
http://www.oneworld.com/ffp/lounge-access
The carrier surcharge for award flights has been discussed to death, BA imposes carrier surcharges on other oneworld partners as if it was a BA flight.
If you want to pay AA's additional fees/charges, then credit flights to their program, although I would hazard a guess that a lot of your BA avios are from credit card bonuses rather than flights..
The text you've quoted means access will not be allowed. I am not sure if BA has more relaxed rules when connecting on two longhaul international flights from business to economy.
Connecting longhaul business to longhaul economy does not allow lounge access at the connection point under oneworld rules.
I'm not so sure about that. It doesn't say that a LH to LH
doesn't qualify.