If you gain an amount of life "for each" of something, that life is gained as one event and Firesong and Sunspeaker's last ability triggers only once.

If a source you control with lifelink deals damage to you, you gain and lose that much life simultaneously. Your life total doesn't change.

Firesong and Sunspeaker's last ability doesn't trigger if a triggered ability of a white instant or sorcery spell or card causes you to gain life, such as the triggered ability of Renewed Faith when it's cycled.

If a red and white spell you control deals damage and also instructs you to gain life, Firesong and Sunspeaker's last ability triggers twice.

If a red and white spell you control deals damage to multiple things using the word "deals" only once, Firesong and Sunspeaker's last ability triggers only once. Similarly, if a red and white spell's effect causes it to deal damage to one thing and then deal more damage with a second instance of the word "deals," Firesong and Sunspeaker's last ability triggers twice, and so on.

A spell causes you to gain life if its cost or effect instructs you to gain life or if an instruction in its cost or effect is modified by a replacement effect and the modified event includes you gaining life. If a spell's cost or effect instructs a source with lifelink you control to deal damage, that spell causes that life gain as well.

If a white instant or sorcery spell you don't control causes you to gain life, Firesong and Sunspeaker's last ability triggers.

The last ability of Firesong and Sunspeaker can't target a planeswalker or battle.