Is there any legit positive impact of LEGO on mental health? Is there any legit research done on the impact of LEGO on mental health? 

For instance, does it positively affect kids’ mental development or does it help with stress, anxiety or any other mental-health issues?
Yes.

Here is a study that demonstrates one way to use LEGO in ADHD counseling.

If you are looking for a more rigorous outcomes-focused methodology, there's another study that looked at the impact of LEGO on social skills development in children. It found significant improvement compared to the control in a pre-test, post-test study.

If your interested in the developmental side of LEGO, here's a study that shows a correlation between complex LEGO play in 3 and 4 year olds and their secondary school mathematics achievement.

On the adult side, here's a study that shows a decrease in workplace stress after a group LEGO activity.

I'm sure there are loads more, but that's what a quick search on Google Scholar turned up.