Can swimming in a lake once cause a brain-eating amoeba infection?
"Brain-eating amoeba" generally refers to Naegleria fowleri. Whether one can get infected by Naegleria fowleri from swimming in a lake depends on whether the lake water is contaminated and on personal protective measures. Infection may occur if the water is contaminated and proper protection is not taken, while infection is unlikely if the water is clean or appropriate precautions are taken. Detailed analysis is as follows:

If the lake water is contaminated with sewage or feces containing Naegleria fowleri, especially in still or poorly circulated water with suitable temperature, the amoebas can survive and multiply in the water. Failure to wear swim goggles or earplugs while swimming may allow the amoebas to enter the body through nasal passages or eye mucous membranes, or through open wounds on the skin, thereby increasing the risk of infection.
If the lake water has been tested and meets water quality standards, meaning it is clean, and swim goggles and earplugs are worn to prevent water from entering the nasal passages and eyes, and if there are no skin wounds, the likelihood of infection with Naegleria fowleri is low. Clean lake water contains very few amoebas, and appropriate protective measures can block the entry routes of the amoebas, reducing the chance of infection.
It is important to wash the body promptly after swimming. If symptoms such as headache, fever, or eye discomfort occur, seek medical attention immediately for evaluation.