When initially introduced Lifelink was a triggered ability. If a permanent had multiple instances of lifelink, then each of these separate abilities would trigger independently ultimately causing the controller of of these abilities to gain more life than the damage dealt.

However when the Magic 2010 base set was released how Lifelink works was changed. Lifelink is now a static ability that changes what happens when a permanent with lifelink deals damage. Instead of dealing damage and the ability triggering as a separate item on the stack, the damage is dealt and the controller of the source with lifelink will gain an equal amount of life at the same time. Because of this change, multiple instances of Lifelink are now redundant. For example, if a Baneslayer Angel that is equipped with a Basilisk Collar deals damage, the controller of the Baneslayer Angel will only gain five life, not 10.

Keep in mind that some older cards have abilities that are similar to lifelink but are not actually lifelink. If a card were to gain mutiple instances of a non-keyworded triggered ability that is similar to lifelink, then each of these abilities will trigger. For example, if the ability of a Genju of the Fields resolves multiple times, then the animated land will end up with this multiple instances of this lifelink-like trigger. Each of these abilities will trigger independently and the controller of this animated land will gain life equal to the amount of damage done times the number of times that this ability has resolved.