my guess is [...] you could counterfactually save 1-5 more lives per day by volunteering and being great at your job. 

I'm skeptical. That would mean that your average hotline volunteer is speaking to 1-5 new people per day who subsequently take their lives, but would not have if the call were handled better. This seems implausible purely on the basis that most suicide attempts fail (5-11% of people who ever attempt end up ever succeeding). Added to this, I suspect that some (most?) people who call are thinking about suicide but not literally about to do it, some (most?) are making multiple calls to the hotline, and that some of the worst cases may be possible to save today but will take their lives in a few months' time. Basically, I suspect that each call that a volunteer successfully handles would be worth more like 0.001 or 0.01 of an averted suicide.

I did (non-suicide) helpline training once and was struck by how formalised it is. Volunteers were supposed to be listeners, reflecting the callers' thoughts back to them and avoiding giving advice. This is likely a strategy to minimise the harm caused by layperson volunteers interacting with very vulnerable people. I would suspect that suicide hotlines have fairly rigid guidelines on how to handle calls, probably with more specific training on how to help the caller de-escalate their suicidal thoughts in the moment. My concern would be that this leaves little wiggle room for being "great at your job", and anyone trying to be significantly more effective may actually do damage by going off-script.

Would love to hear from someone with direct experience!

I answered calls for Samaritans for about a year, and answered texts on Shout for about the same amount of time before that. From my own experience, I'd say 1 to 5 lives per day is extremely optimistic, for the following reasons:

• The vast majority of callers are not planning to take their lives right at that moment / imminently. People call for all kinds of reasons - e.g. loneliness, bereavement, being in prison and that sucking, trying to stop self harming, etc. 
• The majority of calls are from repeat callers (and a significant minority are misuse of the service). Only a few are calling for the first time. (Samaritans doesn't track people, but people often just say they call regularly. Shout did track people. I forget the exact % of conversations that were not first time users but it was definitely most.) And this is obvious right - if someone calls 20 times they generate 20 more calls than someone who calls once.
• For people who really are at severe risk, the reduction in the probability of suicide from one call is pretty unclear, but is certainly much less than 100%.  Even for someone who eventually works through what they're dealing with, it will probably have taken many calls, use of other mental health services, reliance on friends etc., probably over months or years.

I'm not aware of any trials of this kind of intervention, but they could be done. E.g. introducing a new hotline service in a country that doesn't currently have one, but only for a randomly selected half of districts/counties/states, and then comparing the impact on suicide rates over time.

My own unscientific feeling from doing this was that I probably helped a lot of people feel better that day / deal with some kind of crisis, but probably directly prevented very few suicides, if any.

My first question would be: is the particular suicide hotline you're looking at currently turning people away/making people wait a long time because of lack of volunteers? If so, every extra person could be very valuable.

If not, you might be replacing a less skilled volunteer. The question then becomes, how often would you save a life when they wouldn't? That's a hard question and it's not easy for me to know the answer, but it's probably not every night. Lots of people call a hotline with their mind already made up one way or the other.

I did some math here, but now think that I was terribly optimistic and I took people's self-reports about helpfulness too seriously. Maybe it's still useful as an upper bound.