That assumes that people from happier places don't commit suicide as often as people from less happy places as you put it - I doubt that's true. Lawyers think they work hard, but they are far from unique. Auto mechanics very often work 70hrs a week and many, many other professions also require hard and long work.
I'm not the least bit concerned and won't be offing myself any time soon
If being a lawyer becomes something that makes me unhappy, there are a million other things I could do with my self that would be preferable to being dead.
It is a somewhat high-stress, tedious job I suppose, but that suits me fine. One, possibly contributing trend in law school and perhaps practice is additional measures to help those who have difficulties emotionally/psychologically to deal with the stress of law school and to adjust law school demands wrt scheduling, time to take an exam etc, to suit them. I suspect that this kinder, gentler, more caring approach to law school does these individuals a disservice. In the old days where law school was supposedly hard and those who couldn't stand the pressure dropped out or failed out. Now law schools, with the best of intentions, help them through law school. I doubt legal practice has gotten any easier so those folks now become lawyers and then find themselves without the support and coddling that is available in law school and maybe some resort to suicide. There are of course strong counter arguments to this hypothesis - some of those who recieve help in law school may overcome their difficulties and become able to withstand higher stress levels, some may simple commit suicide as a student rather than an attorney if law schools were less gentle, and I'm sure there are many more. Still, I suspect there may be some empirical merit to the hypothesis that if law school were harder/more stressful it might weed out, at a time when stakes are much lower, those who can't deal with the stress and ultimately result in fewer suicides.
As for the 3L course, I think no one would take it. You could make it mandatory, but then you'd waste most or all of the student's time. Most law schools have extensive programs to help students learn about mental health issues. I'm doubtful as to how helpful these are, in part for the reasons suggested in the prior paragraph.