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.
I was never stressed before becoming a parent. My job pressure is the same but the combined stress is what hurts.
Flexible work hours, remote work and a strictly never-over-40-hours work week has been absolutely essential to be able to cope and still be a good parent (hockey practice weekdays at 4 twice a week for example).
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.