I think trying to solve personal (e.g., non work related) problems is a minefield. I would not, as a team lead, go there beyond a generic offer to talk. Most companies likely have standard policies for health and similar personal issues and trying to make your own policy on any serious issue there can backfire badly.

But job-related stress is there and is often solvable (e.g., a developer may be stressed if he committed to a a week's worth of work done in 2 days, etc.). My 2c.