That doesn't sound like the right way to drive an LED from what I understand. LEDs are current mode devices and the "voltage" on an LED is only approximate. My understanding is that you either need to set up the LM317 as a current source (such as shown here: http://www.reuk.co.uk/LM317-Current-Calculator.htm
) or have a series current limiting resistor. This circuit can be use to drive 1 LED or several in series with the same current spec assuming the voltage can be supported by the LM317 and source voltage.
If you drive an approximately 2.2V LED with 2.2V "exactly" the LED will either poorly light or could draw too much current and possibly burn it out quickly. I guess you could measure the current and see if the voltage was too high or too low.
I'm not an expert with LEDs but I am an EE and every LED circuit I have seen has a current limiting resistor or has a current (not voltage) source. Plus I did a little studying before putting LEDs into my Schuco signal lights.
This link is one (of many) references on the need for a current limiting resistor: http://led.linear1.org/why-do-i-need-a-resistor-with-an-led/
well some red LEDs have a forward voltage of 1.7 some are 2.2. When you set the voltage of the regulator to 2.2 you don't need a resistor for the 2.2 volt LEDs and only a small one for the 1.7 volt LEDs.