From the Super Mario Wiki
A Commander Lakitu is a Lakitu that appears as an enemy in Mario & Luigi: Dream Team. Commander Lakitus don't appear on the field due to their nature as a background enemy and only appear at the start of battles involving Boomerang Bros. In battle, they appear in duos and command Boomerang Bros., directing how they should attack. They can only be defeated if Mario or Luigi throws a Taunt Ball at them, however doing so will make the Boomerang Bros.' attacks harder to avoid.
When commanding in one instance, the Lakitu will fly in a varying kind of circle to signal the Boomerang Bros. to throw their boomerangs in a similar fashion to how the two Lakitu fly. If there are two or more Boomerang Bros., the two Lakitu may raise a red M flag and green L flag, one raising one and the other raising the other. As they do this, the Lakitu move towards or away from the battle simultaneously.
If they fly in a clockwise (when looking from the Bros.' point of view) circle, the boomerang will fly towards Luigi first. If counterclockwise, it will fly towards Mario first. If the Commander Lakitu floats downwards and does two clockwise loops, the Boomerang Bro will jump then throw (this being another indicator of a jump throw), and the boomerang will fly towards Luigi first, however it flies the Bros. heads for the first loop, where they must idle, and then jump when it flies towards Luigi the second time. If it does this with counterclockwise loops, it will fly towards Mario first, and he must jump first on the second loop.
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