Protection prevents damage, so protection will be unable to prevent damage while Sunspine Lynx is on the battlefield. However, this won’t allow spells or abilities to target permanents they wouldn’t ordinarily be able to target because of protection, even if that spell or ability would deal damage to those permanents.

Spells and abilities that cause players to gain life still resolve while Sunspine Lynx is on the battlefield. No player will gain life, but any other effects of that spell or ability will happen.

Sunspine Lynx only stops damage from being prevented by effects that specifically use the word “prevent.”

If an effect says to set a player’s life total to a number that’s higher than the player’s current life total while Sunspine Lynx is on the battlefield, the player’s life total doesn’t change.