Mom complains of pain in her skin?

Update:  after reading the other posts on medical side effects, you might ask her oncologist about the side effects of the meds she's getting, or if you know what they are, research them online yourself.

These are good suggestions; I hadn't even thought of the cancer med side effects.

I'm so sorry to learn of this, and of how upsetting it must be.

My sister developed a resistance to touch when she was also in stage 4 of metastatic breast cancer.   Her feet were subject to a different situation; by the time the metastasis was that severe, she had developed drop-foot and walking was very difficult.  I don't know how much of that aspect caused pain.

The pain worsened with a pleural effusion, but continued until her passing.    She just couldn't stand to be touched.

I really don't know what options there might be, but I would make it clear to her medical team that she doesn't want a morphine solution at  this point.

One thing that really did help my sister though was that the Infusion Center had a visiting Reiki practitioner.   It was so helpful that she also asked for it during her last days.  

Here's some info on Reiki if you're interested:

http://www.reikiconnectionmiami.com/  

This one seemed a better company than some of the others I've found (I only did a quick check ), but if you do want to pursue this, I would ask nurses at the Infusion Center affiliated with the hospital, or ask the nurses at the performing doctors' practices.   Or even call other hospitals' Infusion Centers and ask around.

BTW, this isn't what I would consider as New Age practice; it's a founded Japanese method, if I understand correctly.

I have two thoughts on this problem. Often chemo drugs will cause neuropathy which is nerve damage which can cause tingling, burning pain, usually in the feet and legs. I'm not certain what can help with that pain as it is caused by actual damaged nerves. The second thought is somewhat related. I once had horrific burning pain on the skin of my leg. It felt like the worst sunburn you could even imagine but there was no sunburn or any kind of redness or hotness on my leg. I couldn't stand to have a sheet touch it or take a shower or have a pair of pants touch it. Even a light breeze blowing by was excrutiating. They determined it was a nerve pain of unknown cause. I used a drug called Lyrica which is often used to treat pain due to diabetic nerve pain and shingles. It worked and the pain never returned. I can tell you from my experience that it is real PAIN but there is absolutely nothing anyone can see causing it. I would definitely talk to the doctor and see if there are alternate medications that might help her. My heart goes out to her.

Is she also diabetic? DH let his diabetes get out of control and he began having these horrible 'under the skin' itching. It was a type of neuropathy. He was actually CHEWING on his hands and wrists, the itching was so bad. I asked Dr. SIL who said, quite simply "His diabetes is not in control. This is going to be how he feels as long as he chooses to be non compliant".

Just got his diabetes back under some control and the itching ended. SIL also says many drugs will cause this--it's not dangerous but it's horribly annoying.

Is it possible that the brain is sending false signals that the foot hurts?
the chemicals used to treat cancer can damage other areas of the body.
Does the Hospice mom is with offer Reiki Therapy? It is a Japanese Technique that can promote stress relief and "healing" It can be a hands off therapy so there would be no touching of an area that is sensitive. (I personally have not tried it but if it might be of help anything is worth a shot even if it relieves a bit of the discomfort.)
I have read pro's and con's about it but if it can not hurt why not try it?
(This would not replace current medical advice just add to it)

I have been doing some searching but nothing comes up in regards to foot and/or skin pain related to late stage lung cancer. I'm assuming the foot pain is in both feet and all of her foot, not just a certain area? Asking because I found this article but it relates to early stage lung cancer:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5471084/