I'm not sure about the origin of the name of the bulgarian leva but the name of the Romanian leu has it's origin in the 17th century. One of the currency used at that time was the dutch leeuwendaalder(lion thaler) which had the dutch lion engraved on one face. Colloquially the currency was known as the lion.

Later in 1835 Alexandru Ghica introduces the first official Romanian currency known as leu.