It comes from a 1970's british TV commercial for Lemon Squeezy detergent. They were with a little girl who points out dirty greasy dishes to an adult (mom or relative) and then this adult produces Lemon Squeezy and they clean the dishes quickly. At the end of the commercial the girl says "Easy Peasy Lemon Squeezy".
Today it is a silly way to state something was or will be very easy.
12 step recovery jargon referring to someone new who talks about how great life is, now that they'resober. Usually meaning that the person is out of touch with reality.
The new guy seems pretty happy for a dude who has no job, no money and no family. He must be on a pink cloud.