Living in the Fast Lane means that you live for the moment, you don't worry about consequences, or what would happen if something went wrong.
What living in the fast lane means
The saying comes from the multiple lanes of a highway: With a 'fast lane' being the one where vehicles travel at the greatest speed.
This lane is usually used to overtake other vehicles, but "living" in this lane would probably mean having a wild lifestyle... Usually things like drinking lots, having sex, and taking risks.