How much of a chance is it for me to get lung cancer if three people in my family got it?

Higher than normal. There are several reasons why a family history of lung cancer may increase your risk. The members involved may share similar habits like smoking or if they live together and everyone who does not smoke gets exposed to smoke from at least one smoker. Also if the family lives in a place where they are exposed to carcinogens such as radon. Genes may also play a role but not well defined as of yet.
Genetic. Counseling is indicating if any of you were less than 50, occured without a history of smoking in any of the members of your family, and with three, there is enough evidence unless all were heavy smokers and over age 60. Needless to say, while no one should smoke, certainly no one in your family should.