Definitely not! Mercury can cause neurological damage amongst other things. You and your dog may not die necessarily, but I wouldn't want to end up with brain damage, as mercury crosses the blood-brain barrier. Whenever I take my dog swimming, one of the first things she does is drink the water. Methyl mercury is the type of mercury found in lakes and fish, and it is the most toxic form of mercury. You definitely shouldn't go swimming in that lake, especially on a regular basis because mercury can build up on the body, but I wouldn't even take the chance once. Mercury takes a few months to leave the body.