Simply.. my thoughts are with you.

I just went through this recently. I told the truth. I said, "I don't pray. But, I will
keep good thoughts for you, which is the exact same thing."
I'm not really sure how the other person felt about it, but they haven't asked
me to do it since.

I do not have to respect religious beliefs, but I can still respect the individual.
That is also a two-way street. If you want respect, you have to give it, too.
You can't expect anyone else to respect your (general) religious beliefs, if you
are unwilling to respect that others may not share them, or believe anything.

"I'm sorry to hear that. Keep me updated." Then you don't have to lie. If you're close enough, I'd throw in a "let me know if there's anything I can do" as well.

there at peace now not hurting anymore.

if its really going to hurt then I would just lie

Just say your thoughts are with you.

I usually respond with, "I do hope all goes well for them...this us such a hard time for you...call me if you need a shoulder." That covers you for the empathy and says nothing about any sky god...and offers path that is non-combative which at that moment is really needed. The ones that get me are the ones that send me "prayer chain requests" for some random thing they pulled off the net... REALLY? And keep in mind these people KNOW that isn't gonna happen...but they just can't seem to accept reality(which seems to be both symptom AND problem if that's possible) ... What I really want to respond with is, "sure, I'll pass that shit on to the trees and the grass and the stars and the moon for you!" They just don't get it...and there better not be a prayer request about the Orange Obscenity in The White House...I WILL LOSE. MY. SHIT!
If I'm caught up close and personal and have to do the "prayer circle" BS ... I just link up and say nothing...and maybe think of some of the beautiful places I've been or the best lovers I've known...that keeps it in perspective for me...
If someone is really hurting I am there as a shoulder...if they are being obnoxious and disrespectful they will get a mirror.
Namaste

‘I’ll do everything I can, but that won’t help.’ But fortunately, my family are Atheists.

It’s just a plea for support. We don’t have to get caught up in what we think someone means by it. I always say “ sending vibes” . Just so the person is aware of the support. I don’t have any conversation in my head that “ I don’t pray so I can’t support the request or I will support them but not like that.

Tag along, say yes to give them peace of mind and take the win knowing you don't have to do ?

I usually say, "There is a power for good in and around all things, including your husband. This power is acting right now to create the perfect outcome."

I would say I'm thinking of them. Which is true. I don't pray.

None of my loved ones will ever think to include me in a such text , they know better . ?

I usually just say I'm sending them well wishes or healthy thoughts. I'm very open about being atheist though so I think pretty much everyone knows.

If they know you're an atheist, they may just be including you on the text to keep you in the loop. I don't generally respond to group texts unless I'm sure a response is required, and it this case, I would think, as some of the previous responses, a phone call might best address the person's concerns.

I would just say sure thing. It doesn't seem like this would be a situation where it is prudent or necessary or sensitive to make an issue of differing beliefs.

I would say:
"While I don't believe in any deities in the sky, I do sincerely hope that the Doctors and Nurses who attend Chris are fully focused on their work and have the greatest skill to help this situation resolve successfully".

I usually say that I hope the doctors are amazing and are able to help.

I just tell them I'm thinking about them and maybe send good wishes.

I don't think one has to assert themselves at that point. As others have suggested, one can provide support in such a situation without betraying themselves: He is in my thoughts, I remain hopeful, wishing him only the best in care. I've experienced even being in a prayer circle. While I bowed my head, I was thinking about my "to do" list for the day. The religious or religion controls your mind only if you let them or it.

I always say, "sending love and light."

shes worried about her husband and must not know about your standing on prayers etc i would just send a thoughts are with you hope all goes well txt then at some later point when emotions are not running high let her know you don't feel able to do so or not if you are planning on not having that discussion.Now is not the time to appear to be a dick her emotions will make it way bigger than it needs to be good luck

Say that you will pray for lord Baphomet as they asked. They will never ask again.
If they say that you should pray to god, you choose any famous pagan god and say that you will pray to it.
If they insist about the real god you say that there are no real gods, and they should be more specific about which imaginary friend you should pretend to have a telepactic conversation.
If they say lord Jesus or the christian god, at this point you might just laugh that they are trying so hard.

If it's an immediate family member then I would text, "I hope he gets well." If it is a distant family member or non-family, then I will ignore it for not showing me respect for my beliefs.

That’s not my ball of wax, but I wish you the best possible outcome.