My heater keeps cutting off pilot and shuts down. There is no air in the lines! Thought maybe it was the safety shut off switch or thermostat.

Yes, it is a safety shutoff. More than likely the Oxygen Depletion Sensor (ODS) is clogged with dust, lint or pet air.

To clean it, turn the gas line feeding heater off. Remove the front part of the heater cabinet. This will expose all of the inner workings. You'll probably find a lot of dust and lint, so use a vacuum cleaner with a hose and brush attachment to vacuum all the areas you can safely reach. Do this gingerly. Look for the Pilot Assembly (it won't be hard to find). Using Canned Compressed Air and the Straw Nozzle (Like you clean your computer with) hold the can as upright as possible and place the straw nozzle just into the tip of the pilot. Give a quick blast of air. Now, look down the pilot from the tip and you should see a hole in the side of the pilot. That's the ODS. Place the tip of the straw nozzle just barely into the hole and give it a quick shot of air. That will blow out any debris.

Reassembly the cabinet, turn on the gas line, purge the air from the line by pushing the control knob down and holding down for several minutes. Let off the knob, wait 5 minutes and try lighting the pilot. If it does light immediately, there may still be air in the line. Continue to try lighting until you get a pilot flame. Hold the Control Knob in for at least a minute, slowly let off. If the pilot stays lit, turn the Control Knob to On. That should solve your problem. If it doesn't, you may need to replace the thermocouple.