Presumably your company has other accounts; I would tell your boss you don't want to service that account anymore (be proactive and "quit" instead of being fired). I don't know that the other company is/should be investigating you at all since you don't work for them. I doubt you'll get a fair hearing since the other person works for that firm, they'll protect their own rather than a vendor employee?

Don't be "nice" anymore. It's a really ugly thing this person is doing, lying. Don't just "hope" it will be okay, take the offensive and don't stand for it! Lodge your own complaint with your boss and demand he do something about it/protect you/get your duties changed so you don't have to deal with this unscrupulous person anymore.