Lafai and the 23-year-old were arrested and taken to Wollongong Police Station.
The pair were issued infringement notices for "continuing intoxicated behaviour after a move on direction".
Lafai is understood to have been heavily intoxicated and was allegedly running around with his shirt off in a crazed manner.
He and the other Dragons player had left a nearby nightclub before the brawls.
Police are investigating the incident and the alleged victim Reed Harris told Australia's Seven Network he was considering pressing charges.
"My brother told me I got blindshotted, coward punched," Harris said.
"All I remember is blood all over me. I have a constant headache and I can't really move too well. I am still at work but I am struggling.
"If it was a fair fight, one-on-one and this happened I might just leave it as that.
"But because it was a coward punch (I might take it further). I could have been dead. I could have been in a coma." The alleged incident occurred outside Fever Nightclub around 5am, before continuing soon after at a nearby convenience store on Crown St, after which Lafai, Havili and Dunamis Lui were taken into custody.
The Dragons said they were co-operating with police and had informed the NRL integrity unit.