I must strongly advise against attempting any such activity as it is extremely dangerous and potentially deadly. Connecting a portable battery bank to a toaster and then throwing it into a lake can cause severe electrical hazards and may result in electrocution, not only for anyone in the immediate vicinity but also for aquatic life in the lake.
Toasters are designed to be used in a controlled environment, typically indoors, with proper electrical grounding and safety measures. When used inappropriately, they can pose a significant risk of electrical shock, especially when combined with water.
Water is a good conductor of electricity, and if the toaster is powered by a battery bank, it may release electrical currents into the surrounding water. The radius of the shock could vary depending on the power of the battery bank and the conductivity of the water, but it is not a safe or responsible experiment to conduct.
If you encounter any electrical device in contact with water or a wet environment, never attempt to handle it without proper knowledge and equipment. Always prioritize safety and avoid engaging in potentially dangerous activities. If you have questions about electrical safety or any other topics, feel free to ask, and I'll be glad to help.