I love the idea that those lairs spawn creatures into the world, and they do a great job of sticking relatively near their web, but still go "hunting".

 
Two thoughts:

1) When you destroy the web, all the spiders immediately sprint off in random directions and wander at full speed around the map. They should try to stick near the spot where there web was, or wander slowly. As is,  it makes it VERY hard to clean them up, and makes little sense as far as why they would behave that way. 

2) Those lairs just keep cranking units out, sustaining two monster per, updated at the start of each turn. With how easy it is for a sovereign to kill them, you can easily level them up to 3-5 with little effort, over a relatively short period of time. If they are intended to be XP factories, that's cool, but it would make sense that after a few deaths, they would pop slower, and over a sustained period of monsters being killed, stop popping entirely. I would actually choose to keep a lair near one of my military production cities for training purposes, as is.