Pain describes as “burning” is usually nerve related and can be circulatory system issues as well. Inform her PCP for a neurology referral. Most likely she’ll have lower extremity doppler studies or an EMG to diagnose. Does she have peripheral vascular disease as well? Usually gabapentin or lyrica is prescribed and does provide relief, per many patients of mine. Good luck!
See what you come up with under "paraesthesias of lower limbs" or "of legs" on google. I haven't personally encountered burning. See a lot of restless leg syndrome, a lot of tingling, a lot of numbness, but burning sounds more rare. Interesting. Let us know if your sleuthing comes up with anything. Did you run it by the doc? Are there circulatory problems or is there edema on these limbs? Stretched skin can cause some problems but usually the elder doesn't have a whole lot of sensation lower limbs.
My mother has non-diabetic peripheral neuropathy in her legs and experiences pain/burning/numbness/heaviness in her legs & feet after lying down, and especially during the night & after waking up in the morning. Neuropathy is nerve damage which is irreversible, unfortunately. Gabapentin helps a bit, but not entirely. She takes 600 mg at bedtime which also helps with sleep. Penetrex cream helps my mother quite a bit. You can purchase it online at Amazon.com A neurologist can give your LO a physical exam to determine what's going on. Mother has had this condition for the past 30 years and the first signs are the pain/burning in the limbs, then loss of balance, difficulty walking, and the inability to feel the feet which leads to falls. Neuropathy is often associated with diabetes, but can also come about for other reasons, as in my mother's case.
Best of luck!