True kennel cough virus lasts 3 weeks regardless of treatment and disinfecting measures. However, if you were having other dogs around, your best bet is diluting bleach or roccal. Lysol does not work as well, and is much more toxic to animals.
As for the dog, severe coughing can last when the virus is gone due to irritation if the cough itself wasn't treated in the meantime. The antibiotics are to ward off secondary infections only, not to treat the kennel cough itself. (It's important for avoiding pneumonia, basically).
The cough can be controlled to lessen irritation by giving some Robittusin DM (no other variety) at a dose of 0.5 to 1.0 mg per pound of body weight (start with the lesser dose) no more than once every 12 hours. You can read about the drug here:
Controlling the cough this way should bring quick relief of the irritation. In the meantime, I would also only use a harness instead of regular collar with leash, to avoid further tracheal irritation and coughing!
Let me know if I can help further, and hope your dog is better in no time!