I can understand that because your lease stated that you could not smoke, you just naturally assumed it was a smoke free environment. But, the wording is kinda tricky because it says YOU cannot smoke, not that there is NO smoking in the entire dwelling. I would think the same as you thought, a smoke free environment.
However, the lease only pertains to you, not everyone else in the dwelling.
I would have my doctor write a note that due to medical reasons, you cannot live in a smoker's house and he recommends that you move. Present that to the landlord and see if you can get out of your lease, stating that you mistakenly were under the impression it was a smoke free home because otherwise, you would have never rented the unit to begin with.
This is such a pity because you were mislead. However, I have to wonder about something. Like most people, especially those who dislike cig smoke, I can smell smoke on people and can tell if a house contains smokers. I am curious as to how you possibly missed that your landlord smelled of smoke and how you did not recognize that he smoked in the house.