Lifelink is defined as follows:
702.15b Damage dealt by a source with lifelink causes that source’s controller, or its owner if it has no controller, to gain that much life (in addition to any other results that damage causes). See rule 119.3.
Attacking a Planeswalker deals damage to it.
510.1. First, the active player announces how each attacking creature assigns its combat damage, [...]. A player assigns a creature’s combat damage according to the following rules:
510.1a Each attacking creature and each blocking creature assigns combat damage equal to its power. [...]
510.1b An unblocked creature assigns its combat damage to the player or planeswalker it’s attacking. [...]
510.2. Second, all combat damage that’s been assigned is dealt simultaneously. [...]
Whatever additional effects the dealing of damage may have (loss of life, gain of poison counters, loss of loyalty counters, gain of marked damage, gain of -1/-1 counters, etc) are irrelevant. You will gain life.