I was listening to a podcast recently where there was a quote - unrelating to Everton, but accurate nonetheless - "what you are witnessing on the pitch is a reflection of what is happening in the boardroom"
I wouldn't have hired Lampard because the body of work wasn't there. I liked his coaching appointments though. My instinct is the same as yours, it shouldn't come down to one game and it certainly shouldn't be a rushed appointment if he is fired. But, before we rush the knives out, we need to remember some of those shortlists that led to Benitez and Lampard. This is not a sane, measured process and it's doomed to fail again because there will be some lunatic inclusions that will be considered regardless of suitability.