If that's what she wants, Lilly should get Edgar out of her life until she feels ready to have him in again. That time might be never, or it might be tomorrow, but until that day comes (if it comes) this relationship should be on Lilly's terms.
If Edgar asks her to come to some event, she can just say no. If he asks why, she can say something like "Because I don't want to," "Because I don't respect you," "Because I don't really want you in my life." It might be hard but Lilly can practice not being afraid, and if he gets emotional she can just sit there like a stone. Lilly could tell Edgar that she doesn't feel like forgiving him or having him in her life, and until
she is interested in doing that, he has no business with her. If he persists, Lilly could get a restraining order.
On a safety note, if Edgar is a threat, getting a restraining order is not enough. Even carrying around a cell phone isn't enough. If he's hit people in the past he might do it again. Lilly would be well advised to carry around mace and a loud siren alarm around at all times. Even if the threat is slight, it's best to be prepared.
You might like to read
this webpage.