It really depends on your character. My warrior is my only 100% LS character and what he does, he does to keep the people of the empire safe and prevent genocide by the republic. He's a hero, not an anti-villain. Yes, he believes that the empire is better than the republic, a bulwark against inevitable chaos, decadence and hypocrisy that would be the result of Republic rule, although it's in dire need of change at the top which he has every intention of making happen. Thing is, that doesn't really matter in determining what kind of a character they are, just what they do and why. Whether it's a hopeless task has no bearing on the character's nature.
That almost reminds me of someone you encounter in Act 3 for the Trooper.