Do you think my AC will bring in stray cat illnesses from outside (better explanation in comments

So I have been taking care of a stray cat. Pretty much she is ours now, but until I can get her her shots, and hopefully she does not have any serious diseases like fiv or felv, she will most likely become another indoor cat. For now though we set up a tarp on our back porch. My AC from my bedroom sticks out where the vent goes into the outside is on the porch, so pretty much inside the tarp room where the cat frequents and sleeps. Do you guys think if I just spray lysol in my room periodically I should be ok? With it being summer I would assume like humans animals just don't catch colds as often. Thanks

Lysol is dangerous for both humans and animals, so I wouldn't spray it.  I don't think you'll need to do anything to keep it from getting sick.  Most illnesses (colds, etc) are brought on by stress in kitties.