Multiple instances of lifelink are redundant. Giving the same creature lifelink more than once won’t cause you to gain additional life.

Each time the second ability resolves, a delayed triggered ability is created. Whenever you gain life that turn, each of those abilities will trigger. For example, if you activate the second ability twice (and let those abilities resolve) and then you gain 2 life, each opponent will lose a total of 4 life. Each instance will cause two abilities to trigger, each causing that player to lose 2 life.