I had MP for many years after my C-section. Finally when Lidoderm patches came out, I tried those and I went into a remission. It did flare with my recent battle with drug induced lupus, but only for a few days. The angioedema from the Lisinopril activated it slightly. Also heat (hot tubs soaking) or heating pads were very triggering for it. And also over-extending the leg.

There are many places along the lateral femoral nerve that compression can occur. Where it exits the spine, at L4-L5, may be a source. Then this nerve goes thru the abdomen, and exits
under a ligament along the lateral side of the thigh. It may be compressed there too.

Wearing tight jeans, or having stuff in a back pocket and sitting on it, tight belts, surgical procedures of the abdomen, or bone marrow harvesting of the pelvis can cause this.

If you have both sides equally, affected I'd look to the spine.
Diabetics may have damage to this nerve too.

Here is an article with illustrations. Fig. 2B shows the lateral femoral nerve exiting the abdomen. That is where I applied my Lidoderm patch. Using one every day for about 2 weeks turned off the over-firing of the nerve and I had a remission. I still get twinges now and then but they are brief. And the numbness is almost gone.

http://www.aafp.org/afp/2000/0401/p2109.html

When my pain was the worst, it was like 100 beestings all at once. Or a lightning bolt of searing pain.

When I'd use the sauna at the gym it would flare by the time I got to my car. Just stretching that leg to get in the car was painful sometimes. So I avoid heat because of that.

Supplements for this would be fish oil/krill oil for its anti-inflammatory effects. Avoidance of compression triggers, avoidance of heat triggers, having your B12 evaluated, Vit D, etc.

Try putting an ice pack on your lower back twice a day, and see if it is helpful. Or put it over that lateral side of the upper thigh.
You can perhaps find your compression location that way.