We want to get a puppy and we asked our landlord if we could. We even said we would pay a pet deposit. After thinking about it she said no due to bad past experience. However in our lease it does not say if we can or cannot get a dog. Can she legally tell us no?

I have requested this be moved to another section of this forum, please bare with us, hopefully someone can answer for you shortly.

Moved to Real Estate Law.

Are you ready and willing to move when your lease is up ?
That is what will happen if you move a dog in against the landlords permission.

Can you, I would believe you could , since the lease does not say you can't. But the landlord will most likely look for any and every reason he is allowed to use to evict you. If you are one day late with the rent, or if there is too much trash around the house. Are you in violation of any city code. As a landlord I know there are 1000's of loop holes to evict someone if I really wanted them out, for example if they made me mad.

But at the very least, they will just not renew your lease and ask you to leave.

So perhaps you should just wait till the lease is over and move to a dog friendly place.

Also expect if you get a dog for a list of dog damages, including getting any dog "scent" out of the home in case the next renter is allergic

I don't think she can prohibit what isn't in the lease, but she can use everything in the lease that covers what the puppy might cause - noise and damage inside and out, basically. She can do whatever she wants when the lease term is about to end too, from jacking the rent sky high to terminating your tenancy. It just isn't wise to get into an adversarial relationship over this.
Put a request in writing with all possible situations you promise to not let happen, from barking to chewing to scratches of toenails to cleaning up feces in little baggies while walking him on a leash and not just letting him out in the yard. Think of everything. If you both have jobs, what do you plan to do with a lonely barking puppy who also needs to be walked? If you are both gone all day, you shouldn't get a puppy anyway.