Some considerations in making this decision: Would she expect you to tell her? How close is she with her dad? Do you think he regrets telling you? How much does the image of her parents’ marriage play a role in your own?
If keeping this from your wife will create a barrier within your marriage – and it’s easy to imagine how it could, whether it’s because you two have a healthy level of emotional intimacy or you just have a lousy poker face – then you should tell her. It could be complicated by the fact that she’ll never get to hear her mom’s take on it. There could be confusion, anger and grief, as well as friction with your father-in-law. But emotional fallout can be worked through in time, while carrying the secret might never get easier.
Has this been a sudden change in your sister? If so, I’d worry about underlying depression, anxiety or other health or emotional problems.
In that case, you’d owe it to her not to disappear but to express your concern: “You haven’t seemed to be taking good care of yourself lately. I’m worried about you. Talk to me.”
If she’s always been somewhat this way, and is otherwise healthy, then, as her sister, you still owe it to her to explain your distance. “Our lunches haven’t felt like they’ve gone as smoothly lately. I don’t want to hurt you, but you’re sometimes a little hard to be around.” Depending on your closeness, you can either subtly joke about the details or let her fill in the blanks – and hope she’s receptive to your message.