California: can I refuse to rent to a smoker who says they won't?

[Eliot Hochberg]

I have a tenant who signed a no-smoking lease in Los Angeles. When I asked them if they were a smoker, they said no. 

The other day, I saw them smoking in front of the building next door. Today, they were smoking in front of my building. It's a duplex, and I live downstairs. The sidewalk is about 25' from my front door, and also about 6' lower.

As far as I can tell, they don't smoke in their unit or on their balcony.

I'm pissed because they lied to me about being a smoker. 

Here are my questions:

First, can I evict them for lying about being a smoker, even though they are technically fulfilling their lease?

Next, am I allowed to ask them not to smoke on the sidewalk in front of my property?

Third, in future, can I refuse to rent to someone just because they are a smoker, even if they promise not to smoke in the unit?