The price of loving something, is the pain you feel when you lose it. When it comes to animals, you need to recognise the fact that you will lose them, and guard your heart against the day when it will happen. With 50 years' experience of loving and losing, I know, it hurts. Raising baby animals and sending them on to new homes hurts too, but you still have to show them love so they know how to give it back. Accept the pain, cry when you need to, and move on.
It sounds like you were still very much in love with your Lacey when you lost her. It's not fair to have lost her before the "new" wore off. It isn't fair that her life wound up being so short. She was completely yours - you found her, you paid for her, to have invested so much time and emotion in her only to have her life end so abruptly and so soon really stinks. It's perfectly understandable that you are angry. Anger is part of the grieving process, but you seem to be stuck there. Being mad at Luke won't bring Lacey back. She's dead, even if Luke weren't there, she'd still be dead. It sounds like it was a quick death, at least she didn't suffer.
When something you love leaves you or dies, it leaves a hole in your heart. Nothing and no one will ever fill that hole. Each new love creates its own space, it doesn't "replace" what was lost. But loving something else can ease the ache of that void, and make it play a smaller part in your life. Learning how to deal with loss is part of growing up, and it's something we all have to deal with in our own way.
Your father was trying to help with the hurt when he bought Luke for you. Yes, it was too soon for you. You wanted a "suitable mourning period" before you moved on. That's understandable, some people work that way. It was a bit clumsy on your father's part, but he meant well. If thinking of Luke as your sister's dog, or the family dog, or something like that makes it easier, go with that thought, but Luke needs to be loved for who he is. He isn't the dog you were so in love with, but he is a lovable dog.
Chances are, even with the best of care, Lacey wouldn't have had a long life. Long, low doggies are prone to back problems that tragically shorten their lives; their owners get faced with "that decision" all too soon in most cases. Be glad for the time you had with her, it sounds like she was a real sweetie. Try to remember things about her that make you smile, and don't let her loss cast such a huge shadow on your future. Loving others isn't a betrayal, its an affirmation of how much she meant!
