Piccolo teaching the Saiyans how to be lawful evil actually makes sense to me. Raditz's squad is a demonstration of how things operate. The Saiyans aren't that evil, or they just lack finesse. They're a bunch of thugs who fight for sport and to show others their might and strength. I mean, they'd still be cruel towards others, but they'd do so indiscriminately and without restraint. It seems like Saiyans only became the rulers of the universe after Frieza because of the bragging rights and didn't give a damn about maintaining their position. I remember that Universe 3 was in chaos when the Saiyans ruled it because everyone was too individualistic and had no long term goals for their empire.

This is what made Frieza a more fearsome ruler of the universe vs. the Saiyans. Frieza knows the extent of his might, power, and his capacity for evil. If he has no use for somebody, someone irks him, or he needs to demonstrate or remind his might to others, he has no problem committing evil. He kills others only when it's necessary if it would further his long term goals in conquering the universe. It's a universe in order through Frieza's tyranny, but a universe in order nonetheless.