Evaluations after the reforms suggest that they saved lives. A study by Andrew Leigh of Australian National University and Christine Neill of Wilfrid Laurier University estimated that buying back 3,500 guns per 100,000 people led to a statistically significant drop in firearm suicides — 74 percent, in fact, with no parallel increase in non-firearm suicides. ...

The results on homicides were a little less clear. Leigh and Neill found that the buyback resulted in a 35 to 50 percent decline in the gun homicide rate, but because of the low number of homicides in Australia normally, this change wasn't statistically significant

I don't have the numbers for Austrialia, but from the same article:

Nearly two-thirds of gun deaths in the US are suicides

If the proportion in Autralia are similar, reducing gun suicides, if not homicides, could save many lives.