In other words, if I cut a deal with my nearest pirate, does that just mean that lair or a few lairs are my friends, or are all lairs now friendly to me across the galaxy? Being at non-aggression doesn't get me sight of all lairs so if I find a new one will it and its ships be hostile? 

It gives you a non agression pact with the whole pirate league, which means all pirate ships will ignore you and only the nearest lair will pressure you in case of a Pirate Mark. Care though that this non-aggresion state is kinda fragile because when one empire improves relations with pirates, other empires lose some of their positive relations value. So be sure you pay them in time :)