My Friend Blames Himself for my Boyfriend Hitting Me?

I recently got out of a bad relationship with a guy I had been dating for about a year, we are both 19. I broke up with him because he started getting physically controlling and during the very last argument we had he gave me a swollen lip and a huge bruise across my chest. Well our last argument was of course pretty bad, he accused me of cheating on him with my friend Lance (who I’ve known my entire life) . I told him the truth, that I never cheated on him and that me and Lance had been friends for years and there was no reason why I couldn’t hang out with him anymore. That’s when he started getting physical and I broke up with him. Well I wasn’t planning on telling Lance about any of this because for one thing I was embarrassed, and because I didn’t want to have to confront him with a huge bruise on my face and it didn’t seem like a very appropriate thing to discuss over the phone. Well it turns out he found out anyways because my ex showed up at Lance’s apartment and tried to beat him up and I guess he bragged about hitting me and told Lance that if he didn’t leave me alone he’d make his life a living hell. Yesterday Lance showed up at my place and was freaking out. He said he couldn’t believe that I’d be with someone like that and that I should call the police and then he kept asking me if he was always hitting me. Lance spent most of the day with me and he kept acting as if it was his fault that this happened, I think he blames himself because I met my ex through him (they were never friends, my ex was more of a friend of a friend) . Well then Lance started trying to get me to go to the doctor because he said if my chest hurt that bad there could be something wrong but I just didn’t want to deal with that I know its just a bruise and it only hurt when lance accidently bump into me with his arm. Im sort of not sure how to deal with this situation. Lance is afraid that my ex is going to show up at my place again so he basically wont leave my side and I feel bad because he’s acting so guilty and he keeps saying hes sorry he let this happen. I don’t know how to convince him that Im fine and that its not his fault, my ex hasn’t called me or anything and I don’t think he’s coming back but Lance is still freaking out is acting really protective. What can I do to make him under that NONE of this is his fault. Ive told him before that this isn’t his fault but I feel like that’s making him feel even worse.