"This is a tragic accident and serves as a reminder to all to act in a safe manner when out socialising," a police statement said.
A close friend of Ms Greer's family told the Herald yesterday that Ms Greer's mother, who lived in Australia, was devastated.
The friend, who declined to be named, said she only knew what the police had told her about the incident.
"My only comment is that it is a silly, silly mistake ... a very, very silly accident.
"I know that there are probably a few rumours going around, but what I have been told by the police was that it simply was an accident."
The incident is not the first time people have been injured after falling from Lion Rock.
In 2010 two men, aged 18 and 31, suffered critical injuries after falling more than 60 metres after walking up the rock just after midnight.