I really can't tell what's going on unless you provide more specific details. What are these "white lies" and what do you mean that they don't matter? We need to know more in order to know what's happening here.
I'm a lot like you, I don't handle lying well, and I used to over-react about it. I had a boyfriend who would tell white lies if he thought I might get mad at him, so, for example, once I opened my leather polish and noticed it was half gone, so I asked him if he had used it and he said he didn't. I knew that he did when I asked him, so there was no point in him lying to me. It was a rhetorical question that meant, "I wish you had asked me before using my leather polish," but he was so defensive that he always went straight for denial. Stuff like that drove me crazy and I saw it as his immaturity and inability to handle adult conversations because of cowardliness. After I had had a few more relationships, I was a little more forgiving because it seems like all men do at least a little bit of that defensive behavior when they think that they're in trouble. I think TheBF did it just last week! I was looking at pics on LPSG and he saw one on my screen of a female and said, "Is that you? Did you upload a photo of yourself?" I said, "No... Is that what you think I look like? Do I look like that?" He began backpedaling immediately, claiming the photo was so small and he was so far away from it that he couldn't see it very well, etc. I let him off the hook. I suspect those are white lies, but he doesn't want to hurt my feelings and it really doesn't matter. The only part that really bothers me is if he is lying then that means that I don't look as good as I thought I did, and that bothers me because I was feeling good about how my body looks, but that's MY issue and it has nothing to do with lying or about him at all.
So, as far as the lying thing is concerned, can you tell us more? And also, what's going on with you beating people up? Don't do that. What's the story there?
Some people just have a hard time believing that someone would love them, so they doubt it, is there something like that going on?