Can a person with lazy eyes see clearly?

It depends. Lazy eye can mean an eye that does not see well despite proper prescription lenses being used. It can also mean an eye that is not aligned. In the first case, the lazy eye usually does not see better than about 20/40. In the second case, it may have the capacity for 20/20 vision but the brain is not utilizing the information from the eye while it is turned off-axis.
Maybe. The definition of amblyopia is decreased vision in the absence of true eye disease. So, the "lazy eye" does not see well but the other eye can often see normally. It is rare for patients to have amblyopia in both eyes but it does happen.