I have seen differing statements on lysol working or not working, I honestly don't know. Coccidia are a protozoan type parasite and are different from other kinds. A 10% ammonia solution is supposed to work (1 part ammonia to 10 parts water) on hard surfaces. Nothing is going to eradicate it from the soil. I clean my brooder with straight vinegar and let it air dry. I also use vinegar on feeders and waterers to clean. I sanitize my incubator with Simple Green D Pro5, which takes care of bacteria and fungus's and many virus's, it does not mention coccidia (not a big worry for an incubator).
I would remove all the bedding/shavings material and dispose of them. Clean the brooder well, scrub off any dried droppings with hot soapy water. Rinse and dry and then treat with the ammonia solution. Give it time to air dry completely and for all fumes to dissipate. Same with feeders and waterers. Keeping the brooder clean and dry is the best prevention. Wet bedding is prime for an outbreak, as well as letting droppings build up. Keep feeders and waterers as clean as possible.
If you have coccidia in your environment then one way to help prevent illness is to give your chicks a dish of soil from your yard ( not from the chicken area), in the brooder, every day starting in the first few days after hatch, so that they can scratch and peck and dustbathe in it. That exposes them to all the microbes in your soil and gives them a chance to build up some resistance while their immune systems are forming. If they are in a sterile brooder with zero exposure, then the odds are they will become ill once they go outside and are in contact with the soil. The idea is to expose them gradually, rather than with a heavy load all at once. I've not had an outbreak in years by doing that. I still keep treatment on hand just in case. Immune systems can differ, some may be more susceptible than others, and some strains of coccidia are more virulent than others.
