Determining current through LED light
3V on the LED is what you'd expect from a white LED.
Forget about the 9V supply. Instead use a USB &quot;charger&quot; ie a 5V 1A power supply. This should be much more useful as you'll be able to plug the light on a powerbank, on a cellphone charger in the car, etc. Also the resistor power dissipation will be manageable.
Cut a USB cable and connect to the lamp's PCB on the battery terminals. 3 AAs is close enough to 5V so it should work.
Otherwise you can connect the LED directly to the 5V with a resistor. Assuming the &quot;500 lumens&quot; are &quot;cheap lumens&quot; let's go for 3W. So that's 1 Amp at 3 volts on the LED. With a 5V supply, that leaves 1.9 volts on the resistor and 0.1 volts on the cheapo USB cable, total 5V. A 1.9 ohms resistor will do the job. It will dissipate close to 2 watts, so get a 5 watts model. It will get pretty hot. With a 9V power supply you'd need a 6 ohms resistor, and it would dissipate 6 watts, that would be a problem.