Unable to light up all the LEDS connected to Arduino using processing
I'm guessing it is a hardware issue as I discussed in the comments above. 

I have just set up a breadboard and copied your code verbatim into the Arduino IDE and Processing (I edited the port index to use). It works as desired. Pressing R, G, or Y will turn on the respective LED and releasing it will turn it off. 

I can press these three keys in any combination of none on, one only, any two, or all three, and the LED gives the expected result. 

Keyboards were not initially designed to have multiple "main" keys pressed down at any one time, the exceptions to these being the modifier keys (Windows/Command, Option/Alt, Control and possibly some others (I'm thinking the older keyboards here that had "other" keys—Scroll Lock, Print Scr, etc—I'm really unsure). 

It appears now, that some hardware and software may have overcome this. As I've said, your project works fine for me. Also, you could try three different keys, it could be a result of how the keys are scanned and you may stumble across three that don't interfere with each other. 

As I've suggested in the comments to your question, modify the code to utilise the modifier keys instead, or use the keyboard keys as toggles (ie press once for on, press again to turn it off).