I think it's so great that you are going to lunch with your friend.
We lost my nephew when he was 10 to cancer. What was most helpful was just anyone reaching out, like you did.
The only things I hated was when people said things like, 'God only gives you what you can handle'. Or as others have said, 'Everything happens for a reason.' I HATED those two lines. I never ever say those to other people. They were so hurtful to me.
The other thing I hated is when people probed for questions, the answers of which would really help themselves and not the grieving party. Like... what were his initial symptoms (that was a biggie) or what was the treatment. I found it really rude and all about them.
I really hated that. I know this isn't your situation. It's not a horrible thing to be petrified that a horrible tragedy will fall upon oneself or one's family, and I have definitely felt anxious after hearing of someone else's tragedy, but the way to handle that is to do one's own research (google, podcasts, anything), but not ask the grieving family. One friend in particular kept calling with such in depth questions of how my nephew was diagnosed and (before he died) questions about his treatment (she wasn't a doctor or in the medical profession whatsoever). It really enraged me at the time. Now I look back and think she was just anxious for her own children and didn't know what to say and didn't mean to hurt me at all.
Or when my sister would give me very general statements to pass on to friends and family, 'treatment is going as well as it can' or awful things like that, some relatives would respond with such pointed questions, asking my nephew's chances of survival and what exact brain cancer he had, long before my sister clearly wanted to share anything more. I hadn't pushed her for more information so they shouldn't. People say the stupidist things.
I agree to make it 'normal' and let your friend take the lead. Often, when people lose someone, they talk about the 'sad eyes' that others give them. It's just exhausting to always have those sad eyes at you. On the other hand, when I've been the one trying to comfort another person, I really get that it's weird not to be sad - as in, I don't want to act in a way that makes my grieving friend think I don't care or understand how tragic the situation is - so it's such a fine line. I do think that it's nice to follow her lead and keep it light if that's all she wants.
This is a total aside, but I had a friend who was having an affair and very torn up about it. When we would get together, I would ask her questions - I thought I was helping, since she was so upset and I thought I'd somehow be leading her to some decision - and then one day she yelled at me and said to stop asking her questions and... I realized that she did *not* want to talk about her affair. She wanted a normal lunch where she could forget about how messy everything was in her life. Here I thought I was being supportive to try to help her come to some decision to get out of this horrible angst, but she just needed a reprieve. I totally got it wrong by her book.
Other responses - I actually loved when people said that they were thinking of me or praying for my family (and I'm not religious). Oddly, my mom didn't, so I guess people react to things differently.
I also liked when people said something about my nephew, either when he was alive, or about him, or that they were thinking of him.
A friend remembered the day my nephew died a year later and wrote an email and I was so touched.
One friend, after my nephew died, said, 'I just can't believe it. Your sister has everything, good connections, jobs, good salary. If anyone could save him, I thought they could.'
I know that that was a brazen thing to say and many people would hate it, but honestly, I loved when she said that because my sister and her husband are very impressive and I understood what she meant. I had been thinking the same thing. Maybe I liked what she said because it was just so true.
One last thing - I think any resources you can give (especially if your friend wants them) would be useful. For instance, where I live now, there is a center for kids who have lost a family member. If I were helping someone here, I would tell them about the center in case they would want to seek support for their kid. Or maybe to find out about suicide surviving family support groups and just jot the information down in case you get a sense when you see your friend that she would want that information. Many people probably wouldn't, but the worst thing is the shame on top of the grief and I hope your friend gets support.
I will be thinking of her. And all these beautiful responses from people who have lost loved ones. I'm sorry for your losses.