Does this really work to color hair?

Ive heard of lemon juice to bleach it. Because I really dont wanna damage my hair!): I want to get two big chunks under my hair and die them purple, and pink. My mom wont be on the same page if I have to bleach because she doesnt want me to damage my hair. I have dark brown hair, that looks auburn in the sun.. Is there any safe bleaches coz lemon juice is kindaa ghett o, okay ALOTghe tto lol! I also want a dye that will last for along time. Ive had color before but they wash out and turn a nasty crappy color!/: So if you guys can tell me how to bleach my hair without damaging it( like an all natural bleach) And some colors that last for a loooongggg time(: Thanks in advance guys;D