I am not sure how polluted the lake water is. This is indeed a big question.
However, pollutants in swimming pools are restricted by laws (at least where I live) and I FULLY agree with what is written in the article that you mentioned: https://swimswam.com/how-much-pee-is...s-if-you-dare/
In swimming pools, the same water that goes out through the gutter, comes back over and over. The water is looped back into the pool. In my area, outdoor pools are filled only once a year, and indoor pools 3 times. Any type of dirt, contaminant, dead cells, hair, grease, sweat, secretions stay in the pool unless properly disinfected or removed. Unfortunately, reaction with disinfectant generates hazardous products. The more people enter in the pool, dirty (or dare peing, pooing, spitting, etc.), the more disinfectant must be put in the water, thus the more there is generation of hazardous compounds/gas that might harm your health on the long terms, but also irritate the lungs on the short term, or promote headaches or eczema, or anything similar.
In my area, the contaminant thresholds ( for instance E. Coli) are sometimes exceeded in some swimming pools. It is very scary. Swimmers MUST clean the whole body, including the head (hair), the feet and the popo BEFORE even entering the swimming area.
Personally, I never enter pools for babies (the shallow ones).