The Romanian currency is traditionally called 'lei', however in Romania, the term 'roni' is also used for money.
RON (Romanian New leu) is the code used by banks for the Romanian currency, similar to USD, GBP, EUR, INR, etc. It replaced ROL (Romanian Leu) in 2005 (see Wikipedia) and for a while people were using it as a name for the leu for making clear that they refer to the new currency. It is used less and less in everyday speech.
The old Romanian dollars (Taleri) actually had some lions on them on the coat of arms, inspired by the Dutch Lion Thaler (leeuwendaalder). Many commoners couldn't read at the time, so they identified the currency by the lions, hence the name.