So, let's say that I have a Dawn of Hope out. I have 2 Healer's Hawks that attack on the same turn. I pay 2 mana to draw a card for the lifelink from the 1st healer's hawk. Do I need to spend another 2 mana if I want to draw another card or do I just draw another card automatically since there were 2 lifelink events in that turn?
Notice that it says "If you do", not "If you did". It is not checking whether you have, at some point, paid 2 generic mana. It's checking whether you paying 2 happened for that trigger. Every time you gain life, Dawn of Hope puts a "You may pay 2. If you do, draw a card." on the stack. Each time such a trigger resolves, you either pay 2 and draw a card, or nothing happens. If, theoretically, there were a card that says "Every time you gain life, you may pay 2. If you have paid 2 this turn, draw a card." or "You may pay 2. If you do, for the rest of the turn, draw a card every time you gain life." then you could pay just 2 to draw two cards. But this card is worded as "Each time you gain life, you may pay 2 to draw a card", not "You may pay 2 to draw a card every time you gain life".