Let me get this straight. You want our scouter, who is down to their last life and just told you about a potential danger to taking out Mewtwo (Lapras), to battle? Even if she were on the trainer side KY would still focus her down first.
Technically I don't take a penalty if I use an area damaging move like Earthquake, so it's entirely up to KY if he's willing to take the penalty to save his Mewtwo for later.
You "forgot"? But you supposedly researched Mewtwo and Articuno earlier. Even if you didn't know Mewtwo has the highest base stats, you would have noticed his speed stat.