I'm not sure what your reasoning is for arrivng 3 hours early at LGA. If its to ensure you make your flight on time, I'd suggest you'll probably be safe with 1 1/2 hours, 2 hours advance arrival max, to clear security & get on your flight.

Now, if you need to present that cert at the airport in order to reserve an upgrade, then you should get there PLENTY early. I would suggest swinging by LGA the day before if you will be nearby to try to check in a day early (you can check-in 30 hours in advance online, so why not in the airport too?), and try to get on the list. But I'd call CO first (as suggested in the previous post) to see what they say. You just might save yourself unnecessary waiting time in LGA.