Oxine is supposed to kill most every organism...even Marek's, I understand. It's concentrated...you only use 6.5 ounces per gallon, but it definitely is pricey to get the gallon. I don't think you're supposed to use lime with chickens. And yes, it's best to get as much biological material out of there as possible.
I've also read that it's an extremely helpful practice to remove your chickens from an area for at least 3 weeks a year, but most of us are unable to do so. I converted a horse stall to a temporary holding area for my layer flock and put them in there for 3 weeks, then sprayed Oxine solution liberally in the chicken run and coop. On the ground, walls, wire fencing, inside & outside the coop, etc. So far, so good...