Lifelink is not a triggered ability. It's a static ability that applies concurrently with damage.
Lifelink will apply interestingly in this situation. Lifelink can only cause you to gain life if you're actually dealing damage. If damage is prevented, it isn't dealt. However, because Ageless Entity now has trample, you can assign 2 damage to Fog Bank and the rest to the defending player. That remaining damage will apply lifelink, but the prevented 2 damage that would be dealt to Fog Bank will not.
November 30, 2015 5:04 p.m.
You will gain life equal to the damage that trampled over Fog Bank.
So, 4 life is what you gain because your 6/6 had to deal 2 damage to the Fog Bank which was then prevented via the Fog's prevention effect and 4 trampled over.