What are the chances of having a lazy eye if I am nearsighted in one eye and farsighted in the other?
Depends. It depends on your age and the level of disparity. If you are a teenager or older and it's not lazy now then it should not become. If you are younger then appropriate correction with glasses and patching (if lazy) should prevent.
Yes, if you're a kid. Lazy eye is amblyopia, a developmental brain problem in which a child's brain gets a better image from one eye than from the other eye. The part of his brain that gets the good image develops normally; but the part that gets the bad image won't develop well, and the corresponding eye won't "see" well. An adult should not get a new lazy eye because the adult brain's vision area is fully developed.