At this point is about the only you can try and hope it hasn't been ran with the contaminated oil too long as fuel/water laden oil can some serious damage internally but it not as bad running them without any oil at all. If it fails then you chalk it up to a good experience as it has already been rejected by someone. At least it isn't brand new engine. I brought one a couple years ago that the guy never put oil in a new engine and it of course thrown a connecting rod through the block. I knew what I was getting as buying it the other new parts it still had good.
If it was here and knowing how kids like to help daddy take care the of the mower it might even be paint. But for I can't smell the difference between straight oil and fuel laden oil anyway; I have tried. I did have one little boy that fill his dad's string trimmer full of water and admitted it later.
