Lysol could be a skin irritant... Buy blanket wash (to protect the blanket's waterproofing, etc.) and wash it in the laundry machine. Hang it up to dry... I'd also recommend buying an antibacterial horse shampoo and scrubbing every inch of her with a curry comb and warm water. Rinse her well. Do it daily for about a week. Since it's cold, use a clean cooler or towel and help her dry off. Don't put the blanket back on while she's still wet.
Is she up to date on deworming, vaccinations, etc.?
If the problem persists, contact your veterinarian.
Also, rain rot is not always "scabby." If it is rain rot, get and antimicrobial shampoo and scrub it. Take pick off the hair and make sure you wash it. I've dealt with rain rot before, and this is what fixes it. Also, rain rot generally has something to do with the horse not getting enough of the nutrition it needs... particularly vitamin A, I believe.
What's her diet like?