Men and women ...have the most stressful life/lives

Either is acceptable, but with slightly different shades of meaning, depending if they share the same stressful life (use "life") or each have their own stressful life (use "lives").

In English you use the plural with physical things that people have one of each, e.g. "Those women have the nicest smiles", "They wore their hats". (This is in contrast to some languages which would use the singular, e.g French Duolingo discussion of "Ils ont porté leur chapeau".)

However it's possible in this context to use "life" as a singular when referring to something shared or common.

As far as references, here's a worksheet by a Professor Sharon Delmendo which discusses shared life vs individual lives.