Timid.
This is because a Timid nature allows Mewtwo to outspeed Adamant Mega Aerodactyl, Modest Mega Alakazam, Modest Electrode, +1 Dragonite, +1 Mega Charizard-X, Mega Gengar, and anything slower.
If using Mega Mewtwo Y, I still recommend Timid because it already has monstrous special attack, and outspeeding another Mega Mewtwo isn't bad either. Use Calm Mind if needed to boost special attack.
I don't play Pokemon Let's Go much, but I know this much.