If a lake does not turn over, Jill would most expect to find high methane levels.
When a lake does not undergo turnover, the bottom layers become anoxic (low in oxygen), which can promote anaerobic decomposition processes. In these conditions, organic matter is broken down by bacteria that produce methane as a byproduct. Therefore, in a non-turning lake, the accumulation of organic material and lack of oxygen would lead to higher methane levels.