I know how stressful it can be when you have all that fighting going on. When Magoo first came to us and we had to deal with the constant attacks it was maddening! It created tons of stress for the other cats and it kept us on the constant alert to try to keep it from happening. As most people know I almost returned him to the shelter because hubby and I didn't feel like we could put our other kitties through it any longer. Not to mention the stress we were constantly under. I understand how you are feeling because you don't want to get rid of her but you come to a point where you just don't know what else to do.
And then along came some PT experts that saved the day!!! It was suggested to me to medicate Magoo. I did not want to do that but it was the last resort. I'm so glad that I did now! What a difference it made for everybody! Something is obviously stressing Lita and you may never ever know what or why she is acting the way she is. She can't possibly be happy when she is so upset with the other kitties either. Maybe she could be like Magoo and need some meds for awhile to knock the edge off of her frustration. I was able to wean Magoo off after several months and I have had no problems since. I do, however, keep a bottle of meds handy just in case!
Maybe you should try this before rehoming. As we all know its very hard to find a good home that you would trust to let her go live in. The meds were a life saver for Magoo and my entire fur and skin family and I hope you give it a try.

If I can answer any questions about the meds or anything else just let me know and I will check back in when I can.
Good Luck!