Having lots of is more grammatically incorrect but still widely used. If you need to answer that on a test then i would use. Has a lot of

I would say that native speakers use both. "Laughing has lots of health benefit" sound a bit more colloquial, but in practice, they appear to have the same meaning and function. Perhaps in an essay, you would use "a lot", and then proceed to list the benefits (implying that the benefits were countable). But both can be used in circumstances where the nouns are countable and not countable. https://www.ecenglish.com/learnenglish/lessons/a-lot-lots-a-lot