A lifeline is a safety feature on a boat, a rope that either protects you from falling off or that you can throw to someone who's drowning. If you stumble off your friend's sailboat into the water, she'll throw you a lifeline.
When sailors need to rescue a swimmer or a clumsy passenger, it helps to have a lifeline handy. And when you receive other kinds of vital support or help — a mobile phone, or a job recommendation, or a scholarship for college, for example — you can also call them lifelines. This figurative meaning has been around since the 19th century, while the "live-saving rope" definition is the earliest one, from about 1700.