Actually I think that I invented this accidentally in 1976 in Brentwood, UK.
I was watching my son play for his school football team against a much weaker school team.
After about our sixth goal without reply, I wanted our team to take it easier on the losing playing and meant to shout "take it easy" but somehow it came out "take it easypeasy".
Strangely, the 5 year olds quickly latched onto this and all started chanting "easypeasy". I had nothing to do with lemon squeezy add-on, which as someone has said came from a UK dish washing commercial and was probably added separately later.
Otherwise, I would probably have added it at the time.
It would be interesting to know if there is a instant of the phrase being used earlier than 1976 and that I had used it heard it before.