Do you understand what this block of code does?
It is triggered by the mouse button being pressed.
Then it determines which pin the mouse button was for.
Then it toggles that pin.

What I am saying is that instead of having code triggered by a mouse button being pressed, which runs code in a mousePressed() function, you can have code inside a different function, keyPressed(), which will be triggered when a key is pressed.

You would need to change the above block of code in your original code to something like the following:

1. void keyPressed(){
2.   int pin = -1;
3.   if( key == 'a' || key == 'A' ){
4.     pin = 0;
5.   }
6.   if( key == 'b' || key == 'B' ){
7.     pin = 1;
8.   }
9.   if( key == 'c' || key == 'C' ){
10.     pin = 2;
11.   }
12.   if( key == 'd' || key == 'D' ){
13.     pin = 3;
14.   }
15. 
    
16.   if( pin != -1 && pin < values.length ){
17.     if (values[pin] == Arduino.LOW) {
18.       arduino.digitalWrite(pin, Arduino.HIGH);
19.       values[pin] = Arduino.HIGH;
20.     } else {
21.       arduino.digitalWrite(pin, Arduino.LOW);
22.       values[pin] = Arduino.LOW;
23.     }
24.   }
25. }

1. import processing.serial.*;
2. 
   
3. import cc.arduino.*;
4. 
   
5. Arduino arduino;
6. 
   
7. color off = color(4, 79, 111);
8. color on = color(84, 145, 158);
9. 
   
10. int[] values = { Arduino.LOW, Arduino.LOW, Arduino.LOW, Arduino.LOW,
11.  Arduino.LOW, Arduino.LOW, Arduino.LOW, Arduino.LOW, Arduino.LOW,
12.  Arduino.LOW, Arduino.LOW, Arduino.LOW, Arduino.LOW, Arduino.LOW };
13. 
    
14. void setup() {
15.   size(470, 200);
16.   
17.   println(Arduino.list());
18.   arduino = new Arduino(this, Arduino.list()[0], 57600);
19.   
20.   for (int i = 0; i <= 13; i++)
21.     arduino.pinMode(i, Arduino.OUTPUT);
22. }
23. 
    
24. void draw() {
25.   background(off);
26.   stroke(on);
27.   
28.   for (int i = 0; i <= 13; i++) {
29.     if (values[i] == Arduino.HIGH)
30.       fill(on);
31.     else
32.       fill(off);
33.       
34.     rect(420 - i * 30, 30, 20, 20);
35.   }
36. }
37. 
    
38. void keyPressed(){
39.   int pin = -1;
40.   if( key == 'a' || key == 'A' ){
41.     pin = 0;
42.   }
43.   if( key == 'b' || key == 'B' ){
44.     pin = 1;
45.   }
46.   if( key == 'c' || key == 'C' ){
47.     pin = 2;
48.   }
49.   if( key == 'd' || key == 'D' ){
50.     pin = 3;
51.   }
52.   if( key == 'e' || key == 'E' ){
53.     pin = 4;
54.   }
55.   if( key == 'f' || key == 'F' ){
56.     pin = 5;
57.   }
58.   if( key == 'g' || key == 'G' ){
59.     pin = 6;
60.   }
61.   if( key == 'h' || key == 'H' ){
62.     pin = 7;
63.   }
64.   if( key == 'i' || key == 'I' ){
65.     pin = 8;
66.   }
67.   if( key == 'j' || key == 'J' ){
68.     pin = 9;
69.   }
70.   if( key == 'k' || key == 'K' ){
71.     pin = 10;
72.   }
73.   if( pin != -1 && pin < values.length ){
74.     if (values[pin] == Arduino.LOW) {
75.       arduino.digitalWrite(pin, Arduino.HIGH);
76.       values[pin] = Arduino.HIGH;
77.     } else {
78.       arduino.digitalWrite(pin, Arduino.LOW);
79.       values[pin] = Arduino.LOW;
80.     }
81.   }
82. }