From where I stand, the thing I do to maintain my mental health incidentally makes me look... "macho" isn't accurate, but "sure looks like he lifts" is. At this point, the evidence for exercise being antidepressant is unequivocal. For instance, this meta-analysis of the effect of exercise on depression finds:

Physical exercise is an effective intervention for depression. It also could be a viable adjunct treatment in combination with antidepressants.

And this meta-analysis finds:

Previous meta-analyses may have underestimated the benefits of exercise due to publication bias. Our data strongly support the claim that exercise is an evidence-based treatment for depression.

Moreover, if you turn your attention to table 2 of the latter meta-analysis, you'll find that resistance training had a larger standardized mean difference (SMD) than aerobic or mixed exercise, but also has the largest 95% confidence interval, so large it's the only one that include 0. However, a more recent meta-analysis focused exclusively on resistance training found:

Resistance exercise training significantly reduced depressive symptoms among adults regardless of health status, total prescribed volume of RET, or significant improvements in strength. Better-quality randomized clinical trials blinding both allocation and assessment and comparing RET with other empirically supported treatments for depressive symptoms are needed.

Caveat: the only mental health issues I have a history with is depression (which almost instantly vanished once I bought a power rack for my basement). In writing this, for completeness's sake, I also looked into anxiety and dementia, which were a more mixed bag: some meta-analysis found no significant effect, but bemoaned insufficiently many sufficiently large and sufficiently high-quality studies, while others found a small effect while also bemoaning insufficiently many sufficiently large and sufficiently high-quality studies. However, the depression, anxiety, and dementia reviews all agreed that exercise was beneficial and generally devoid of adverse effects. For instance, the Cochrane Review on exercise programs for people with dementia, while finding no effect on the dementia, cautiously noted an an increase in the subjects' quality of life... whilst bemoaning the dearth of high-quality studies.

So, yes, the evidence is there for looking macho and not ruining your mental health. You reap extra benefit if your mental malady is depression, but lifting remains beneficial even it isn't.