I would like to add the knowledge that I have gained from research regarding the STK11 mutation in case anyone has any suggestions.

STK11/LKB1 is a gene that act as a tumor suppressor. It activates AMPK which suppresses growth when there is a lack of nutrients and oxygen. This means that NSCLC with inactivation of this gene will continue to proliferate, even though there are no nutrients and no oxygen available.

Researchers have found that having a mutation of STK11 in NSCLC means that there is an accumulation of neutrophils/Myeloid Derived Suppressor Cells (MDSCs) in the tumor microenvironment. Other research has found that MDSCs in the microenvironment causes a lack of response to immunotherapy, which is also what happened to my husband. He received an immunotherapy called Atezolizumab and did not respond to it.
However, some months after stopping Atezolizumab, he received palliative radiation therapy and an abscopal response emerged. The oncologists thought that it was the combination of radiation and immunotherapy that caused a response, which is likely. 
However, I had also given him Ibuprofen at the same time, and later I discovered that research has found a connection between STK11-loss-of-function and activation of COX-2 (the article says that STK11 down-regulates COX-2 and that STK11-loss leads to an upregulation of COX-2), and also that COX-2 inhibitors (like Ibuprofen) might inhibit the proliferation of NSCLC with STK11-loss.
Other research shows that Prostaglandin-E2 enhances proliferation and spread of tumors and leads to immune escape, and that COX-2 inhibitors enhances the response to immunotherapy.
So, it could have been the Ibuprofen that I gave my husband that caused the abscopal response, but heartbreakingly I did not know that at the time and I stopped giving him Ibuprofen and on the next scan there was progression again.

A thing that supports the research saying that STK11-loss causes an upregulation of COX-2 is in our experience that around Christmas last year my husband had pain and stiffness in almost all joints in his body (his knees, his hands, his back, his arms and his neck.. he could hardly turn his head for stiffness and pain) and this makes sense, since he was not receiving any treatment and probably the cancer was proliferating and causing a massive accumulation of Prostaglandin-E2 in his body. A few days after starting on a high dose of Ibuprofen, the stiffness and pain was gone. And I know this is a known effect of Ibuprofen, of course, it is used for arthritis, but since the symptoms were so massive and widespread in my husbands body, it makes sense to me that it was caused by the cancer. Also he has never had arthritis before in any joint.

Researchers have also found that NSCLC with STK11-loss lack STING expression and this also means that it is unlikely to respond to immunotherapy.

Perhaps someone in this forum might have an idea of what might be useful to try out based on the characteristics of this mutation?

Thank you.

I think this new trial might be relevant for you: https://clinicaltrials.gov/ct2/show/NCT05469178

It says "Recruitment Status: Not yet recruiting", but they are recruiting. The status is just not updated in the site yet.

The company started the trial on october 2022, here is the press release: https://www.bergenbio.com/bergenbio-announces-initiation-of-phase-1b-2a-trial-evaluating-bemcentinib-in-1st-line-non-small-cell-lung-cancer-patients-harboring-stk11-mutations/