if an arduino (NANO) specifically sould lock up, does its output pins drift high or low?
Specify "lock up".
As long as you don't break it the micro controller keeps executing a program. In case of a bug that might not be the program flow you wanted. And that unwanted program flow can be anything.... Although the chance of it writing to the outputs (aka changing there state) probably isn't to big but yeah, Murphy is on it's way.
To summarize, there is no "lock up", only bugs. And the behavior in that case is unknown.
askingAquestion:
if an arduino (NANO) specifically sould lock up, does its output pins drift high or low?
Nether, it will stay the same. But as was said micro controllers don't lock up, in fact nether do any computers.
Mm, now I think about it, there is one way to really lock up the Arduino and that's when the clock is removed. That way it will no longer execute any instruction aka everything will stay the same.
No, if you remove the clock signal then the clock inputs float. So every time there is any EMI you will get a pulse into and the code will advance one state, eventually over the millennias of time the code would be eventually run.
I think something similar once formed the basis of a Dr Who plot. 
True true 