Not really. You'll never get more current by adding resistance. By adding resistors in parallel, you were actually lowering resistance.
Since the voltage of a 123 is so close to the Vf of a red luxeon, adding 1ohm of resistance will drop the current only slightly. By removing that resistor (or at least, making that resistance smalller, by adding resistors in parallel), you increase the current slightly. The Vf of the luxeon will go up, but also, the terminal voltage of the battery will drop more under load...eventually, by reducing the resitance, the Vf of the luxeon and the terminal voltage of the battery under load will meet.
The current you get under direct drive depends on the dynamic resistance of the luxeon, and the internal resistance of your power source. A higher dynamic resistance will mean that your Vf will be higher at a given current. A higher internal resistance for your power source means its terminal voltage will drop more for a given load.
The internal resistance of most batteries increases as they become discharged.