My own mother went through this. She kept her 4th pregnancy a secret for almost 4 months because of her sister, who had struggled with infertility for 10 years. It was an unplanned pregnancy with a man she was dating too, so my mom felt it was cosmically unjust and felt rather guilty. My aunt found out indirectly, and in the end, she was more upset about that than the pregnancy itself. She felt offended that my mom hadn't just told her, thinking she couldn't handle it. But I think no matter what my mom had done, my aunt would have had difficult feelings to work through.
Your SIL has been through this experience once before, and perhaps she's further along in her grief process and may be less reactive this time. Your daughter has clearly brought her joy - who knows, she may surprise you and be thrilled at the idea of having another niece or nephew. Even if not, remember it is her path and her pain, and there is no reason for your joy to be minimized because she is not dealing with it well. You have every right to bear a child and to have those that love you celebrate that with you. If her grief is impacting her relationships, then it is her responsibility to process that with the help of a professional if necessary, rather than expecting the family to walk on eggshells. Though handling it gently is a good idea, you really have little control over how she will respond. Telling her alone might give her a chance to know "ahead of time" so she can prepare herself emotionally for the joyful reactions of the grandparents, etc. but keep in mind that one-on-one might also put her on the spot.
If you decide to tell her at lunch, I would validate her painful reaction in the past (and express yours - she may need to gently hear that it hurt you when she withdrew from you), express your love and appreciation for her and your hopes for what your relationship can be this time. Express sorrow for her pain if needed, but don't apologize for being pregnant.
I would probably say something like this. "SIL, I love you so much. You are such a great sister to me and DH and loving aunt to DD. I know DD's birth caused you pain and it pained me to see our relationship grow apart because of that. I am so happy that you are a bigger part of our lives now and I hope that continues. I wanted to meet with you today, because I just found out I am expecting. I didn't want that news to cause you pain. You don't need to say anything right now. I just wanted you to know how much you mean to us, and I hope with all my heart that we can stay close. "