What Is The Origin Of The Phrase "March Comes In Like A Lion And Out Like A Lamb"?

March comes in like and lion and out like a lamb, it's origins are uncertain, due to the fact that this saying is very ancient. The saying  refers to the weather.
So, if the weather is bad and very cold or snowing at the beginning of March, then the end of March (going out) will be calm  or as the saying goes, like a lamb.
However, If the weather is mild at the beginning of the month of March, then it is said that the end of March will end with bad weather.
In fact this is also sometimes referred to as late winter, or late snows, and can destroy the new cherry and apple blossom, which is normally the first to appear.