How do you deal with a family member who lies to you?

My brother is 20 and has a history of ADD. I'm older than him. He was always a troublemaker as a child and has grown into a selfish person who has taken money from his parents and his job. He met a woman online and after only a few months moved out of state with her leaving everything (not much) behind. I helped them with the airfare (I know, big mistake) and still didn't get paid. I really think he's lying when he says they sent a money order since he's lied before. And I think she lies with him too. I think this is going to push the relationship to an end...how do I let go even tho I love him so much. He is my brother.