Lying down flat? That extends the leg and stretches the Lateral femoral nerve.

Mine which is in mostly a remission, will twinge if I over extend the leg doing something, or expose it to heat of any kind.
(hot tub, hot bath, steam room, heating pad, etc).

Try putting an ice pack on your groin area when you lie down.
Or if that is not the trigger, put it in the lumbar area on your back
at L4-L5 area and see if that helps.

A strong magnet may help too... Here is my magnet thread:
http://neurotalk.psychcentral.com/thread118248.html

I sometimes use a strong magnet in my groin area for about 20 minutes if I have twinges lying flat. But not often.

I really fixed my MP pain with Lidoderm patches, applied to the area where that nerve exists the abdomen...at the top of the thigh. I thought that was a miracle at the time! Now I don't need anything often anymore, after years of anguish.