Suzaku is nothing. He is a shit of a man. He is superficial and narrow minded. Assume some man is wanted for "viscously" killing 20 people. Is he evil? Well, that depends on circumstance. If he murdered them because thats all he knows how to do and he has to do something, then how can you call him evil. This is a key difficulty in working towards world peace. Suzaku isn't evil, he is essential a good person, as seen in the beginning. He was and still is courageous and wanting to do what he thinks is right. Think of all the shit he's had to take from both the Britons and the Japanese. He endures in hopes of changing the world; to make it a better world. His hatred for Lulu is from the death of his love -- Euphoria-sama. He blames Zero for it, which is unavoidable since he was the one who (al beit accidentally) ordered the Euphoric Princess to kill everyone. Its understand able. Pussy >> Friends.
As for Lulu, everyone he's helped, aside from Karen, C.C, Suzaku, his sister and himself, was helped because it was in his own best interest. He has done a lot of good, but it wasn't intentional.