I tend to avoid Lairs if I can. They are the most difficult Mission I’ve encountered in the game so far. Frankly I find it easier to let them combine into a Citadel and then take that out in the Great Citadel Turkey Shoot than trying to take out the Lair - which is clearly the wrong way round, but there you have it 
When I did assault them, I had a Lvl 4/6 Squad with 3 Sniper/Assaults, 1 Heavy/Assault and a Techhie or a Beserker/Assault, with a Scarab. The fight takes 2 phases:
Phase 1
Set up a defensive perimeter and wait for the first Siren(s) to come to you.
Get at least 1 of your Snipers up a tower, so that she has clear LoS across the map. Her job is to pick off and disable the most dangerous creature she can see each turn:
- Shoot the Siren in the head to take out its Will.
- Disable the arms of Crabbies.
- If you can, shoot a Triton’s weapon to destroy it - otherwise, shoot it in the head to take down its Will and hope it panics.
Worm firing Chirons are a relief and not worth worrying about, as long as you’ve armed all your squaddies with pistols. Half of its worms will fall down the cracks in the map, the rest can be taken out by the nearest Squaddie(s) with a pistol. They’re an annoyance rather than a danger to you. Goo & Explosive Chirons on the other hand are dangerous! Shoot the bugger in the head asap - and stay under overhanging cover as much as possible.
Remember to drop your tower-based Sniper back down to cover if too many enemies with long-range weapons get LoS on her.
When the Siren appears, here’s where the Scarab comes into its own, because Sirens can’t MC you in a vehicle! So hop your Shotgun-armed Heavy and her support guy into the vehicle and move it as close to the Siren as you can get. Next turn, Berserker hops out and unloads on her with Armour Break, then hops back in again. Heavy drops out, takes a pot-shot with her shotgun, then hops back in again. Repeat until Siren runs and hides. If you have a Tecchie, he can Repair the Scarab for 1WP every time he hops out of the vehicle.
Phase 2
Once you’ve dealt with the first Siren(s) that appear, you can start moving forward. At this point, 2 of my Snipers usually unsling their Shotguns and start leapfrogging - Sniper with SR takes Overwatch; Sniper with Shotgun moves up, rinse & repeat.
Meanwhile, the remaining Sniper stays on her post, overwatching the board for respawns & new Sirens.
Now you treat the advance like a house-to-house, leapfrogging from cover to cover and judiciously using dash etc to make sure you don’t get bounced by a blind bend. If you spot a Siren, take out her head asap.
The Spawnery will usually be in the hole at the top left of the map. Sometimes it’s top right, which can be a pain.
TO DISABLE OR NOT TO DISABLE, THAT IS THE QUESTION:
Personally, I tend not to disable the more dangerous Nasties - I shoot to kill, but only if my long-range Sniper can cover the Respawn Point. That way, I clear out the Nasties in the way, and the Respawns appear far away from me. At that point, taking out their weapons and leaving them to run aimlessly around the map is fine.
It’s tough, though, real tough. By comparison, Citadels are a cakewalk.