I get the frustration. From what I've observed, they spawn in the vicinity of home planets. I've also seen them spread to adjacent systems. That was particularly annoying, as I'd quickly eliminated the pirate lair that spawned next to me, but as soon as I started expanding toward my neighboring empires, I quickly discovered that the AI had not been nearly as effective at dealing with their pirate spawns (Endless AI, in case you're wondering). They'd all reached level 5 with multiple pirate fleets in orbit, many of which eventually travelled down to find my nearby vineships. So yeah, I've also had three of 'em appear in the same general area. I was playing on largest galaxy size, for what it's worth.

I generally don't like even knowing that much about the pirates, to be honest. It feels wrong to me that even before I've scouted a lair, I'm already preparing for them. My early tech picks are almost always related to invasion. Maybe if I wasn't always guaranteed to have a lair show up early game.