Am I on the right track here?
You've got the voltage split correct, but the same current flows through both the LED and the resistor.
bpiphany indicated that the LED is driven with 5.05v over a 510Ohms resistor.
Ohms law: I = E / R :applies like: I = (5.05v - 1.97v)/510Ohms ~= .006Amps
This 6mA current flows through both the resistor and the LED.
You'll need to pick a green LED, then substitute its forward voltage (instead of the 1.97v) into the above
equation to find out how much current will flow through it.
If for some reason you really wanted to drive the LED at 20mA (you don't though, it'll be too bright) then
you'll need to change the resistor to get the right mix.