I'm so sorry this happened. I don't understand the ins and outs of it, but L definitely shouldn't have made contact with your sister under any circumstances. It's such an awful feeling when a previously safe person betrays you, even when it was well meant. I've also experienced my T hurting me when she actually intended the best, but that doesn't change the feelings of hurt and betrayal.

The only way I have of dealing with such feelings is to be honest about them with T. Generally speaking, my T is non defensive and listens and validates how I'm feeling. Over time, talking about the feelings meant the hurt and sadness began to fade. It sounds like it's very early days for you so you're still struggling and talking probably isn't helping much. But keep talking. I know it feels agonising that L can't take your hurt away - I felt exactly this with my T - but it really does start to heal if you're both committed to being honest and genuine with each other.

In my experience, the only hurts that T (indirectly) caused that HAVEN'T healed, are those which I feel unable to talk about much, mostly due to what was going on for her at the time. So I think talking really is the way to deal, but it needs L to be patient, compassionate and non defensive.