I have to fill up the little expansion tank on my radiator once a week from bottom to top. Im assuming this is excessive. Its not on the garage floor and none of my hoses feel wet. So Im thinking its either the headgasket or possibly an lean condition. Anyway my question is could a lean condition cause the eating of coolant this fast? or is it definitely the headgasket. I failed smog last time for hydrocarbons so i know my motor is running way too lean.

Have a look at your oil, if its milky then water is getting into it

If you have an external leak, the cooling system will fail a pressure test. And that test will reveal its location.

Head gasket leaks can be trickier to diagnose. A leak from a cooling passage into an oil passage will form a milky emulsion that will be obvious on an oil change. A serious leak from a cooling passage to a cylinder will produce clouds of white smoke and is also easy to spot. The hard leak to diagnose is a small leak from a cooling passage to a cylinder that is allowing air to be pumped into the cooling system. The only evidence of this may be an inexplicable loss of coolant from the cap lifting to vent excess pressure. If this is happening you'll usually find that multiple attempts to bleed the system over several days release air each time. There are chemical tests for exhaust gases in the coolant that can be used to verify this diagnosis.

I have to fill up the little expansion tank on my radiator once a week from bottom to top. Im assuming this is excessive. Its not on the garage floor and none of my hoses feel wet. So Im thinking its either the headgasket or possibly an lean condition. Anyway my question is could a lean condition cause the eating of coolant this fast? or is it definitely the headgasket. I failed smog last time for hydrocarbons so i know my motor is running way too lean.
i thought running lean meant that your AFR doesn't have enough fuel? If that's the case, not enough fuel causes hotter engine, which causes the nitrogen in the air and excess oxygen to bond into NOx gases. It does not result in excess HC (hydrocarbons)... excess HC is a result of running too rich, which also runs cooler.

I had exactly this situation, but for me the problem was the water pump, with the car on medium RPM and up, the water leaked, change the pump and the problem is over