To answer your question si,
Your op amp output is either +rail, or -rail (or nearly so if its a bipolar output type op amp) as its configured as a comparator, sounds like you already got that bit.
When the opamp output is + current flows through the anode of the led connected to the op amp output (and ok we'll call it a bi colour because it does 2 colours), which we'll say is red, then through the resistor thats connected down to ground, the other led is reversed biased so its off.
Then when the opamp output changes to low (-rail) current flows from the + rail, through the led current limiting resistor, through the led with its cathode connected to the opamp, into the op amp and down to ground through the op amps transistors, at this point the first led is reversed biased so its off.
If you were to toggle the op amps output high and low very quickly, say 50hz, then the led would flash red/green, and due to your persistance of vision you would see the led as being yellow, the combination of red and green.
Hope this clears things a little.
You could use a tri colour led with a few connection changes.