Ecobee3 lite connected to Lennox Pulse G14Q Heat/Air Condition

There should be no problem connecting the C wire from your thermostat to the C terminal in the furnace. Take a look at this diagram, which is a rough approximation of your system.

Notice the cable going to the condensing unit has a red wire connected to the Y terminal in the furnace, and a white wire attached to the C terminal. When the thermostat calls for COOL, it does so by energizing the Y terminal (connecting R to Y). This provides power to the coil of the contactor, which allows it to close the contacts and turn the condensing unit on. The other side of the contactor coil is connected to the C terminal, as to provide a complete circuit.

You'll notice in the first image that two relays in the furnace, the thermostat, and the contactor coil all connect to the same leg of the transformer. This is because the thermostat basically works like a switch, connecting the R wire to the C wire through control circuitry. Anything that needs 24VAC power, will be connected to both legs of the transformer.

Alright, I figured out why it wasn't working. Had nothing to do with ACC not having a lead. I was looking at my setup closely and noticed that only 2 wires were coming up from the motor, but it needs 3. I noticed that there was a wire coming from pin 3, but it was crimped and didn't run to the motor. So I looked at the speed table and decided I wanted to run the Brown wire up. Connected it to pin 3. Now when I short R and G, the fan turns on :)