Say I have a Liliana of the Veil that is also a 3/3 creature (possibly via Enchanted Evening and Opalescence).
My opponent attacks Lilly with a 4/4 lifelink, trample and I decide to block with Lilly.
Does my opponent gain three or four life from her creature?
Ok, so the creature is attacking Liliana. Even with trample, the controller can choose to assign all 4 damage to Liliana. So, the controller gains 4 life.
Also, even if you decided to trample the damage over, it would still go to hit Liliana (she wouldn't be dead yet), since all damage is dealt simultaneously.
What's interesting about the scenario is that Liliana is marked for damage as a creature AND loyalty is also removed for each point of damage.
No matter how your opponent assigns damage, your opponent will gain four life when damage is dealt.
##Assigning damage
510.1. First, the active player announces how each attacking creature assigns its combat damage
702.19b The controller of an attacking creature with trample first assigns damage to the creature(s) blocking it. Once all those blocking creatures are assigned lethal damage, any remaining damage is assigned as its controller chooses among those blocking creatures and the player or planeswalker the creature is attacking
When trample damage is assigned, you must assign at least lethal to all blocking creatures, and any remaining can be assigned to the player or planeswalker. That means your opponent has the following options:
As you can see, the options in this case all add up to the same result: all four damage gets assigned to Liliana of the Veil.
##Dealing damage
510.2. Second, all combat damage that’s been assigned is dealt simultaneously
When the 4/4 lifelink trample creature deals damage, it deals four all at once, rather than dealing three followed by one. Simultaneously, its controller gains four life.
Note that because Liliana was dealt four damage in total, she loses four loyalty counters. This is because Liliana is still a planeswalker even though she is also an enchantment and a creature. Even if Liliana were indestructible, she would still die if she loses all of her loyalty. Gideon, Battle-Forged has an ability that specifically protects him from losing loyalty like this.
They would gain 4 life. The creature will deal 4 damage to Liliana either because all 4 damage was assigned to the blocking creature, or 3 was assigned to the blocking creature and 1 trampled over onto the Planeswalker. This is just an odd case where the creature and the Planeswalker are the same object. Since 4 damage was dealt 4 life is gained, it doesn't matter that Liliana only has 3 toughness.
702.19b The controller of an attacking creature with trample first assigns damage to the creature(s) blocking it. Once all those blocking creatures are assigned lethal damage, any remaining damage is assigned as its controller chooses among those blocking creatures and the player or planeswalker the creature is attacking.
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).
510.1a Each attacking creature and each blocking creature assigns combat damage equal to its power. Creatures that would assign 0 or less damage this way don’t assign combat damage at all.
510.2. Second, all combat damage that’s been assigned is dealt simultaneously.
This means that the 4/4 assigns and deals 4 damage. That means its controller gains 4 life.
There are things that could matter (such as the removal of a blocker if the attacker didn't have trample, or if a blocker has Protection from a quality the attacker has), but there are none in the posted scenario.
702.19b The controller of an attacking creature with trample first assigns damage to the creature(s) blocking it. Once all those blocking creatures are assigned lethal damage, any remaining damage is assigned as its controller chooses among those blocking creatures and the player or planeswalker the creature is attacking
Options:
Either way, four damage is assigned, and four damage is dealt.
