Kid Ink -- Pizza Delivery Man Sues Rapper Over Dog Attack ... and Damages have Mushroomed

Kid Ink's dog viciously attacked a pizza delivery guy and now the victim is suing for a piece of the pie.

Garnik Nazarian claims Kid ordered a pie delivered to his Granada Hills home ... and when he showed up at the front door, Kid's dog -- Louie -- attacked him ... chomping down on his hands, arms, legs, face and other body parts.

Nazarian -- claims Kid should've known Louie was "unusually dangerous" and prone to attack ... and should've kept the animal locked up.

According to the lawsuit ... Nazarian's injuries are so bad, he won't be able to deliver pizzas for a long time to come. So, in addition to medical bills and pain and suffering, he wants lost profits.