In my opinion, you are either getting to much or not enough. Something is wrong,

I hope by now you have called a nurse hotline or found a doctor somewhere , but you should get this checked out as soon as possible.

It could be as simple as the way you slept, or your cannula fell out. I am hoping this was a lung specialist that ordered that for you. That is who needs o be ordering and prescribing oxygen, a lung specialist in pulmonary.

You may be able to go to ER if the headaches do not go away and you can not get to your doctor.
The concentrator putting out your oxygen may need to be checked by the medical provider, to make sure it is doing right,
and you need to look at it and make sure you have the right number dialed up not something lower or higher.
Also, another idea is to check your O2 with your oxymeter and make sure it is 90 or above. (Above is better, below 90 is not good)
If you do not have one , you can get one at most drugstores for about $30-40 . It fits on your finger and measures your o2 level in your bloodstream.
Well, those are all my ideas, I would contact your doctor tomorrow for sure and let him know this. But maybe it will be something simple.
Others here will come up with more good ideas and advice
Hope something works
BJ

What other medications are you taking and when?
Things such as Xanax, Ativan (anxiety medication), and Diazepam (muscle relaxers), and some over-the-counter 'cold remedies' (slow down breathing), are notorious for causing odd headaches.

However, regular headaches that wake you or that occur on waking are a serious matter and you should talk to your doctor about them ASAP.

This might be of interest:
http://www.healthline.com/health/copd/headache#Overview1

This is not normal. In addition to calling your doctor, I would call the supplier and ask them to check the equipment (measure the O2 output) to make sure you are getting the prescribed O2 amount..

My 2: if you were not waking up with headache before O2 and now you do, if follows that too much O2 is the issue:
When you sleep, our breathing becomes shallower, and COPD patients get starved of O2. To compensate, our brains compensate and (night) breathing rhythm and depth increases. This gets rid of CO2 which is paramount. If you get too much O2, your shallow breathing keeps going, while CO2 never gets expelled. Ergo: morning or night headache (which should go away shortly after your normal O2/CO2 exchange resumes).
My guess is that 2lpm is too much for you
But do not take my word for it: talk to you MD

A quick Google search of "too much oxygen cause headache" specifically brought up copd oxygen use. Sounds like you are getting too much. Whatever the mechanism that is causing the headaches, orim's suggestion above makes sense. I'd never heard of a surfeit of oxygen causing headache before but I know for sure an excess of CO2 will since when my bedroom was poorly ventilated I'd often wake with a headache. Certainly get to your doctor over it and maybe try 1lpm until you can get in particularly if you didn't have any night headache directly before using night time oxygen.